Abstract:
A photon emitter including a photon generator configured to generate photons having a first polarization state or a second polarization state, the first polarization state being orthogonal to the second polarization state; and a time delay device which delays photons having the second polarization state with respect to those having the first polarization state.

Description:
BACKGROUND OF THE INVENTION 
     (1) Field of Invention 
     The present invention relates to the field of photonic quantum information systems specifically those using unpolarised photon sources. The present invention is particularly intended for use in quantum communication. The present invention also extends to photon emitters and methods for outputting photons. 
     (2) Description of Related Art 
     In quantum communication systems, information is transmitted between a sender and a receiver by encoded single quanta, such as single photons. Each photon carries one bit of information encoded upon a property of the photon, such as its polarisation, phase or energy/time. The photon may even carry more than one bit of information, for example, by using properties such as angular momentum. 
     Quantum key distribution which is a technique for forming a shared cryptographic key between two parties; a sender, often referred to as “Alice”, and a receiver often referred to as “Bob”. The attraction of this technique is that it provides a test of whether any part of the key can be known to an unauthorised eavesdropper (Eve). In many forms of quantum key distribution, Alice and Bob use two or more non-orthogonal bases in which to encode the bit values. The laws of quantum mechanics dictate that measurement of the photons by Eve without prior knowledge of the encoding basis of each causes an unavoidable change to the state of some of the photons. These changes to the states of the photons will cause errors in the bit values sent between Alice and Bob. By comparing a part of their common bit string, Alice and Bob can thus determine if Eve has gained information. 
     A photonic quantum computer or logic device is a device where gate operations are performed upon the encoded states of a number of single photon pulses in order to carry out some computation task. The single photon pulses will be provided either by an array of single photon sources or, alternatively using repeated emission from a single photon source with appropriate delays. In order for the logic gates to function properly it is often necessary for the photons to have the same polarisation. 
     Photonic quantum information systems are typically sensitive to the polarisation of the light used. For example, many photonic quantum communication systems encode information on the polarisation of the photons by applying a rotation to an initial polarisation state. However, this can only be done if the initial polarisation state is known. In other quantum communication systems, the information is encoded upon the phase of the photons in an interferometer. The components in the interferometer will often be sensitive to the polarisation of the photons. For example, the phase shift introduced by the phase modulator depends upon the polarisation of the photons. Thus photons in different polarisations will experience different phase shifts when passing the phase modulator. 
     To overcome the polarisation dependence of such systems, it is common to linearly polarise the light using a polarising filter. However, this has the disadvantage of reducing the efficiency of an unpolarised source. If for example the source is randomly polarised, this will reduce the bit rate by 50%. This problem is of particular concern for single photon sources where this loss cannot be compensated by increasing the intensity. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to address this problem. Thus, in a first aspect, the present invention provides a photon emitter comprising:
         a photon generator configured to generate photons having a first polarisation state or a second polarisation state, the first polarisation state being orthogonal to the second polarisation state; and
 
time delay means for delaying photons having the second polarisation state with respect to those having the first polarisation state.
       

     Thus, since the photons with different polarisations are temporally separated, they may be treated differently by the following components and system. This allows all photons emitted from the generator to be used. 
     The photon generator may comprise weak pulses from a strongly attenuated laser or a single photon source which outputs single photons one at a time in response to optical or electrical stimulation. The generator may further comprise a polarising beamsplitter. In general photons emitted from the photon generator can have any polarisation direction. For example, some photons will have the first polarisation state, some will have the second polarisation state and others will have a polarisation state which is a mixture of the first and second states. These photons may then be passed through a polarising beamsplitter oriented to produce photons from the stream which either have the first polarisation state or the second polarisation state. The photon source may alternatively supply photons having either the first polarisation state or the second polarisation state. 
     The time delay means preferably comprises a polarising beamsplitter which directs photons having the first polarisation state along a first path and photons having the second polarisation state along a second path and combining means to combine the first and second paths, one of the paths being longer than the other path. For example, one of the paths may comprise a delay loop. If a polarising beamsplitter is provided in the generator, this polarising beamsplitter may also form part of the time delay means. 
     Thus, photons which follow the longer path will exit the emitter after the photons which have followed the shorter path ensuring that the two orthogonal polarisations are separated in time. This temporal separation between the photons allows them to be treated differently in the following apparatus or system. 
     For example, in a quantum communication system, the sender of the photons can encode photons emitted by the photon generator in the two orthogonal polarisations with different signals as they pass through the encoding equipment at different times. Similarly, the receiver of these photons may also distinguish between the two polarisations using their different arrival time. 
     One of the paths of the time delay means may be provided with means to rotate the polarisation of photons passing through said path such that photons from the first path and the second path at the combining means have the same polarisation. This may be achieved by using a polarisation rotation device or connecting a polarisation maintaining fibre such that the slow axis of the polarisation maintaining fibre is aligned to inject the desired polarisation into the following component to which it is connected. In this case the photons have the same polarisation leaving the time delay means. However, they may still behave differently in the sender&#39;s equipment and thus, may still need to be distinguished in time. 
     Instead of comprising two paths, the time delay means may comprise a single path configured to allow photons having a first polarisation state to travel at a different speed to photons with a second polarisation state. For example, this single path may be provided by polarisation maintaining fibre which causes photons which have their polarisation aligned along the slow axis of the fibre to travel slower along the fibre than photons whose polarisation is aligned with the fast axis of the fibre 
     As previously mentioned, if the photon emitter is to be used for quantum cryptography, the emitter will further comprise encoding means, wherein photons which have passed through the time delay means are passed into an encoding means. Such encoding means may be used to encode the photon using quantum parameters such as polarisation, phase, energy/time etc. The photons may be encoded such that they have a certain bit value. For example, photons which are encoded with one polarisation axis may be allocated bit value ‘0’ and those with an orthogonal polarisation axis may be allocated bit value ‘1’. Similarly, orthogonal phase states may be allocated bit values ‘0’ and ‘1’. 
     If the encoding means are configured to encode the phase of a photon, they will preferably comprise an interferometer, said interferometer comprising an entrance coupler connected to a long arm and a short arm, said long arm and short arm being joined at their other ends by an exit coupler, one of said arms having phase variation means which allows the phase of a photon passing through that arm to be set to one of at least two values. 
     The photon emitter may be configured such that the entrance coupler has a first and second input and a first and second output, where the first and second output are connected to said long arm and short arm of the interferometer, and said entrance coupler also provides the combining means for the first path and the second path such that photons which follow the first path enter the entrance coupler by the first input and photons which follow the second path enter the entrance coupler by the second input. In this arrangement, the fact that the first input of the coupler is connected to one of the paths of the time delay means and the second input of the entrance coupler is connected to the other path of the time delay means, results in photons from the first path behaving differently in the interferometer from photons which followed the other path because they enter the interferometer via a different input. This is true even if the photons at the first and second input have the same polarisation. 
     In an alternative arrangement, photons from the first and second paths may enter the interferometer via the same input. 
     In a further arrangement, the photon emitter may be configured such that the first and second paths are multiplexed using a polarising beam combiner which is then fed into the encoding means. 
     The photons may also be encoded using polarisation instead of phase. 
     The encoding means of the above emitter, regardless of whether they are configured to encode information using polarisation and/or phase etc, is preferably capable of performing a different encoding operation on photons generated with the first polarisation state than on those with the second polarisation state. 
     As discussed above, photons with the first and the second polarisation states may behave differently in the encoding means. Thus, by providing encoding means which are capable of performing different operations on photons having different polarisation states, it is possible to encode photons having the second polarisation state with the same bit value as photons having the first polarisation state. In other words, the encoding means is capable of compensating for the initial polarisation state of the photons. 
     Alternatively, photons with the first polarisation state may be encoded with a different bit value to the photons having the second polarisation state. 
     Where the photons are encoded using phase, the modulator in the interferometer is capable of providing a different modulation to photons which pass through the first path than those which path through the second path, such that photons exiting the interferometer have the same phase state regardless of their initial polarisation state. 
     For example, where photons generated with a first polarisation state are introduced into the interferometer via a first input of the entrance coupler and photons generated with the second polarisation state are introduced into the interferometer via a second input of the interferometer, the phase shifts applied by the modulator differ by 180° in order to encode the same bit value onto photons generated with either the first or second polarisation state. 
     Where photons are encoded using polarisation, the encoding means is configured to rotate the polarisation by angles differing by 90° such that the same bit value may be encoded onto photons generated with either the first or second polarisation state. Thus, depending on the bit value selected, the polarisation of photons generated with either the first or second polarisation state may be rotated accordingly. 
     The present invention may also be used to produce a source of polarised photons from an unpolarised source. This may be achieved by providing a polarisation rotator which rotates the polarisation of the delayed photons with a relative rotation of 90° with respect to the rotation applied to the non-delayed photons. 
     In a second aspect, the present invention provides a polarisation distinguisher for a photon generator configured to generate photons having a first polarisation state or a second polarisation state, the first polarisation state being orthogonal to the second polarisation state; said distinguisher comprising:
     time delay means for delaying photons having the second polarisation state with respect to those having the first polarisation state.   

     The above polarisation distinguisher may be fitted to a photon generator to form a photon emitter which may be used or adapted as described with reference to the first aspect of the present invention. 
     Since the photon emitter is primarily intended for use in quantum communication system, a third aspect of the present invention provides a quantum communication system comprising:
         a photon emitter comprising:
           a photon generator configured to generate photons having a first polarisation state or a second polarisation state, the first polarisation state being orthogonal to the second polarisation state;   
           time delay means for delaying photons having the second polarisation state with respect to those having the first polarisation state; and   encoding means, wherein photons which have passed through the time delay means are passed into an encoding means,   the communication system further comprising a receiver having decoding means and at least one detector.       

     In quantum key distribution the photons which are sent to the receiver are encoded. Each photon should be encoded independently of the other photons. Thus, if an eavesdropper intercepts a photon she does not gain any information about other photons being sent to the receiver. When a photon pulse is emitted by the generator it will either follow the short path or the long path through the time delay means. Thus, the time when a photon reaches the encoding means will depend on whether the photon took the long path or the short path through the time delay means. The encoding means may be configured to keep the same encoding for a photon regardless of whether it takes the long path or the short path through the time delay means because this encoding will only be applied to one photon. As explained above, the encoding means may be configured to compensate for the initial polarisation state of the photons such that the same bit value may be encoded onto photons regardless of their original polarisation state. 
     The photons may be encoded using phase, polarisation, energy/time etc. 
     Fibre based quantum cryptography systems, often use 1.3 μm or 1.55 μm photons for key transmission due to the relatively low fibre attenuation at those wavelengths. InGaAs avalanche photodiodes (APDs) are often used for single photon detection at these wavelengths. 
     Avalanche photodiodes sometimes produce a response when there is no photon incident upon the device, called a dark count. To minimise the dark count rate, the InGaAs APD can be operated in gated mode, for which the bias of the APD is raised to a value V det2  above its breakdown voltage, thus activating single photon detection, for only the short time period when the signal pulse arrives. The detector time gate d det  will typically be a few nanoseconds wide. In between detection gates, the APD voltage is held at a value V det1  below the breakdown threshold and is thus not sensitive to light. The quantum cryptography system is well suited to gated operation mode, as the arrival time of each signal pulse is well defined. 
     Thus, the quantum communication system further comprises means to apply a gating signal to the detector, said gating signal being provided to switch the detector between an ‘on mode’ where photons may be detected and an ‘off mode’ where photons may not be detected. 
     In the above system, photons which are generated with a first polarisation state are separated in time from photons which are generated with a second polarisation state. Thus, a photon which is generated with a first polarisation state and follows a first path will arrive at the detector at a different time to a photon which was generated with a second polarisation state and takes the second path. 
     The detector may be gated on for the time when it expects to receive a photon which has followed the shortest path through the time delay means, until and including the time when it expects to receive a photon which has followed the longest path through the time delay means. Alternatively, the detector may be gated on only during the two time intervals when a photon is expected to arrive after following either the first or second paths through the time delay means and be in an ‘off mode’ for intermediate times. 
     The said encoding means of the quantum communication system may be configured to encode the phase of a photon and comprise a first interferometer, said interferometer comprising an entrance coupler connected to a long arm and a short arm, said long arm and short arm being joined at their other ends by an exit coupler, one of said arms having first phase variation means which allows the phase of a photon passing through that arm to be set to one of at least two values, the receiver comprising a second interferometer, the second interferometer comprising an entrance coupler connected to a long arm and a short arm, said long arm and short arm being joined at their other ends by an exit coupler, one of said arms having second phase variation means which allows the phase of a photon passing through that arm to be set to one of at least two values. 
     The at least two phase settings of the first interferometer preferably occupy non-orthogonal phase bases, for example one setting may be 0° while the other is 90°. In this case, a key may be distributed using the B92 protocol as explained in GB 2368502. 
     The phase variation means of the first interferometer preferably may be able to set the phase of a photon to one of four settings. Preferably, two of the four settings will occupy the same first basis whereas the other two settings will occupy a second basis, the first basis being non-orthogonal to the second basis. For example, the four settings may be 0°, 90°, 180° and 270°. In this case, a key may be distributed using the BB84 protocol as explained in GB 2368502. 
     Five or more settings may be used to allow encoding using intermediate basis as explained in GB 2368502. 
     The phase variation means of the second interferometer may be able to set the phase of a photon to one of two settings to select the measurement basis. For example, the receiver can use 0° or 90°. Typically, two detectors will be used, one connected to each output of the second interferometer. 
     When using the above system with the BB84 communication protocol, generally, the bit values associated with a particular detector differs between photons generated with the first or the second polarisation state. 
     When using the above system with the B92 protocol, generally, the detectors are used to distinguish the retained measurements for photons of the first or second polarisation state. 
     Only photon pulses which pass through the short arm of one interferometer and the long arm of the other are of use in distributing the key or other information between Alice and Bob. Thus, preferably, the detector is configured to ignore signals from photon pulses which pass through the long arms of both interferometers or the short arms of both interferometers. 
     The detector may be further configured to detect only those photons which pass the long arm of one interferometer and the short arm of the other. Thus, the detector may be gated in an on state only during the arrival time of photon pulses which pass the long arm of one interferometer and the short arm of the other interferometer. 
     Alternatively, the system may further comprise directing means configured to ensure that photons which have passed through the short arm of the first interferometer are directed down the long arm of the second interferometer and photons which have passed through the long arm of the first interferometer pass through the short arm of the second interferometer. 
     Such directing means may comprise first polarising means configured to allow photons which have travelled through different arms of the first interferometer different polarisations and second polarising means which distinguish between the photons having different polarisations and direct them down the appropriate arm of the second interferometer. 
     To optimise interference, it is desirable to ensure that photon pulses which take the short arm of the first interferometer and the long arm of the second interferometer take the same time to pass through both interferometers as photon pulses which pass through the long arm of the first interferometer and the short arm of the second interferometer. This may be achieved by providing means to vary or tune the path length of at least one of the arms of the interferometers. 
     The emitter and the receiver need to be synchronised. This may be done by communicating a clock signal between the emitter and receiver. 
     A clock pulse may be sent from the sender to the receiver with each photon from the generator. 
     The clock signal may have a different wavelength to that of the photons emitted by the photon generator and may be multiplexed and sent along the same fibre to the receiver. 
     Alternatively, or additionally, the clock signal may have a different polarisation to that of the photons from the generator. The clock pulse may also be delayed relative to the photon pulses from the generator, so that it can be detected in the receiving apparatus at a different time. Alternatively a timing reference may be used as the clock. 
     The detector is preferably an avalanche photodiode detector. 
     In a fourth aspect, the present invention provides a method of outputting photons, the method comprising:
         providing a photon generator configured to generate photons having a first polarisation state or a second polarisation state, the first polarisation state being orthogonal to the second polarisation state; and   delaying photons having the second polarisation state with respect to those having the first polarisation state.       

     Preferably, the above method further comprises separating photons having the first polarisation state from those having the second polarisation state. 
     The method may further comprise rotating the polarisation of the delayed photons by 90°. 
     The method may further comprise passing the photons through an interferometer and modulating the delayed photons as they pass through the interferometer such that photons which initially had the first and second polarisation states emerge from the interferometer with the same phase state. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will now be described with reference to the following non-limiting preferred embodiments in which: 
         FIG. 1(   a ) is a communication system and  FIG. 1(   b ) is a schematic plot of the probability of a photon being present in a pulse received by a detector against arrival time at the detector; 
         FIGS. 2(   a ) to  2 ( e ) are a sequence of plots against time schematically how Alice should time her pulses and how Bob should gate the detector using the system of  FIG. 1   a  and; 
         FIG. 3(   a ) is a communication system in accordance with an embodiment of the present invention using phase encoding and  FIG. 3(   b ) is a schematic plot of the probability of a photon being present in a pulse received by a detector against arrival time at the detector; 
         FIGS. 4(   a ) to  4 ( e ) are a sequence of plots against time schematically showing how Alice should time her pulses and how Bob should gate the detector using the system of  FIG. 3  and in accordance with an embodiment of the present invention; 
         FIGS. 5(   a ) to  5 ( e ) are an alternative sequence of plots against time schematically showing how Alice should time her pulses and how Bob should gate the detector using the system of  FIG. 3  and in accordance with an embodiment of the present invention; 
         FIG. 6(   a ) to  6 ( f ) are an alternative sequence of plots against time schematically showing how Alice should time her pulses and how Bob should gate the detector using the system of  FIG. 3  and in accordance with an embodiment of the present invention, 
         FIG. 7(   a ) is a communication system in accordance with a further embodiment of the present invention using phase encoding and  FIG. 7(   b ) is a schematic plot of the probability of a photon being present in a pulse received by a detector against arrival time at the detector; 
         FIG. 8(   a ) is a communication system in accordance with a further embodiment of the present invention using phase encoding and  FIG. 8(   b ) is a schematic plot of the probability of a photon being present in a pulse received by a detector against arrival time at the detector; 
         FIGS. 9(   a ) to  9 ( e ) are an alternative sequence of plots against time schematically showing how Alice should time her pulses and how Bob should gate the detector using the system of  FIG. 7  and in accordance with an embodiment of the present invention; 
         FIG. 10(   a ) is a communication system in accordance with a further embodiment of the present invention using phase encoding and  FIG. 10(   b ) is a schematic plot of the probability of a photon being present in a pulse received by a detector against arrival time at the detector; 
         FIG. 11(   a ) is a communication system in accordance with a further embodiment of the present invention using polarisation encoding and  FIG. 11(   b ) is a schematic plot of the probability of a photon being present in a pulse received by a detector against arrival time at the detector; 
         FIG. 12(   a ) is a communication system in accordance with a further embodiment of the present invention using polarisation encoding and  FIG. 12(   b ) is a schematic plot of the probability of a photon being present in a pulse received by a detector against arrival time at the detector; 
         FIG. 13(   a ) schematically illustrates an apparatus for outputting photons having a single polarisation in accordance with an embodiment of the present invention,  FIGS. 13(   b ) to  13 ( f ) are plots against time of the operation or operating signals applied to the apparatus of  FIG. 13(   a ) to demonstrate how the device should be synchronised; and 
         FIG. 14  schematically illustrates a further apparatus in accordance with an embodiment of the present invention configured to emit photons having the same polarisation. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1   a  shows a prior art apparatus for quantum key distribution between a sender, Alice  1  and a receiver, Bob  3  connected by an optical fibre  5 . 
     Alice&#39;s equipment  1  comprises a single photon source  7 . 
     The single photon source  7  produces a pulse containing a single photon during each clock cycle. The clock has a repetition period of T clock . The clock cycle is controlled by biasing circuit  9 . 
     The single photons are emitted from said single photon source  7  with random polarisations or a random mixture of two orthogonal polarisations. The single photons then pass through a polarising filter  11  that allows just one linear polarisation to pass. For an randomly polarised single photon source this results in half the incident photons being lost. 
     The polarised single photon pulses are then fed into one input arm of the imbalanced Mach-Zender interferometer  13  through a fibre optical coupler  15 . The long arm  17  of the interferometer  13  contains an optical fibre delay loop  19 , while the short arm  21  contains a fibre optic phase modulator  23 . The length difference between the long arm  17  and the short arm  21  corresponds to an optical propagation delay of t delay . Typically the length of the delay loop  19  is chosen to produce a delay t delay ˜5 ns. A photon travelling through the long arm  17  will lag that travelling through the short arm  21  by a time of t delay  at the exit  25  of the interferometer. The two arms are combined together with a fibre optic coupler  25 . 
     The output of Alice&#39;s interferometer  13  is multiplexed with the bright clock laser  27  at the wavelength division multiplexing (WDM) coupler  29 . The bright clock laser  27  is controlled by biasing circuit  9 . The clock laser  27  may emit at a different wavelength from that of the single photon source  7 , so as to facilitate their easy separation at Bob&#39;s end. For example the single photon source may operate at 1.3 μm and the clock laser at 1.55 μm or vice versa. 
     Bob&#39;s equipment  3  is similar to Alice&#39;s equipment  1  and comprises a WDM coupler  31 , a clock recovery unit  33 , a polarisation controller  35 , an imbalanced Mach-Zender interferometer  37 , two single photon detectors  39 ,  41  and biasing electronics  43 . 
     Bob&#39;s interferometer  37  contains an entrance fibre coupler  45 , a long arm  47  containing a delay loop  49  and a variable delay line  51 , a short arm  53  containing a phase modulator  55 , the long arm  47  and the short arm  53  are combined with an exit fibre coupler  57 . 
     Bob first de-multiplexes the transmitted signal received from fibre  5  using the WDM coupler  31 . The bright clock laser signal is routed to the clock recovery unit  33  to recover the clock signal for Bob to synchronise with Alice. The clock recovery unit  33  comprises an optical detector and other electronics such as an amplifier etc. 
     The single photon signal pulses received from fibre  5  are fed into a polarisation controller  35  to restore their original polarisation. 
     The signal pulses then pass Bob&#39;s interferometer  37 . The long arm  47  of Bob&#39;s interferometer  37  contains an optical fibre delay loop  49  and a variable fibre delay line  51 , and the short arm  53  contains a phase modulator  55 . The long arm  47  and the short arm  53  are connected to a 50/50 fibre coupler  57  with a single photon detector  39 ,  41  attached to each output arm of the coupler  57 . 
     To maximise the interference fringe visibility, the signal pulses at the two input arms of the exit coupler  57  of Bob&#39;s interferometer must be controlled to have same linear polarisation. This may be achieved by using a polarisation controller (not shown) on each of the inputs of the exit coupler  57 . 
     The variable delay line  51  of Bob&#39;s interferometer  37  is adjusted to make the optical delay between its long arm  47  and short arm  53  identical as that between the long arm  17  and short arm  21  of Alice&#39;s interferometer  13 , t delay . 
     There are four possible paths for a signal pulse travelling from Alice&#39;s single photon emitter to Bob&#39;s single photon detectors:
         i) Alice&#39;s Long Arm  17 -Bob&#39;s Long Arm  47  (Long-Long);   ii) Alice&#39;s Short Arm  21 -Bob&#39;s Long Arm  47  (Short-Long);   iii) Alice&#39;s Long Arm  17 -Bob&#39;s Short Arm  53  (Long-Short); and   iv) Alice&#39;s Short Arm  21 -Bob&#39;s Short arm  53  (Short-Long).       

     Bob&#39;s interferometer  37  is balanced so that photons taking paths (ii) and (iii) arrive at nearly the same time at the exit coupler  57  of Bob&#39;s interferometer  37 , corresponding to the central peak in  FIG. 1   b . Photons taking path (i) have a positive delay t delay  (later arrival time), and those taking path (iv) have a negative delay t delay  compared to paths (ii) and (iii). 
     Only photons arriving in the central peak shown in  FIG. 1   b  undergo interference. Thus only these photons are of interest. Bob gates his detectors  39 ,  41  to record only photons in the central peak and not those in the earlier or later satellite peak. 
     By controlling the voltages applied to their phase modulators  23 ,  55 , Alice  1  and Bob  3  determine in tandem whether paths (ii) and (iii) undergo constructive or destructive interference at each detector  39 ,  41 . The variable delay  51  can be set such that there is constructive interference at detector A  39  (and thus destructive interference at B  41 ) for zero phase difference between Alice and Bob&#39;s phase modulators. In this case and for a perfect interferometer with 100% visibility, we can then expect negligible count rate at detector B  41  and a finite count rate at A  39 . If, on the other hand, the phase difference between Alice and Bob&#39;s modulators  23 ,  55  is 180°, we expect destructive interference at A  39  (and thus negligible count rate) and constructive at B  41 . For any other phase difference between their two modulators  23 ,  55 , there will be a finite probability that a photon may output at A  39  or B  41 . 
     In the four-state protocol, which is sometimes referred to as BB84, [C H Bennett and G Brassard 1984, in Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE, New York), pp 175-179], Alice sets the voltage on her phase modulator  23  to one of four different values, corresponding to phase shifts of 0°, 90°, 180°, and 270°. Phase 0° and 180° are associated with bits  0  and  1  in a first encoding basis, while 90° and 270° are associated with 0 and 1 in a second encoding basis. The second encoding basis is chosen to be non-orthogonal to the first. The phase shift is chosen at random for each single photon pulse and Alice records the phase shift applied for each clock cycle. 
     Meanwhile Bob randomly varies the voltage applied to his phase modulator  55  between two values corresponding to 0° and 90°. This amounts to selecting between the first and second measurement bases, respectively. Bob records the phase shift applied and the measurement result (i.e photon at A, photon at B, photon at A and B, or no photon detected) for each clock cycle. 
     In the BB84 protocol, Alice and Bob can form a shared key by communicating on a classical channel after Bob&#39;s measurements have taken place. Bob tells Alice in which clock cycles he measured a photon and which measurement basis he used, but not the result of the measurement. Alice then tells Bob the clock cycles in which she used the same encoding basis and they agree to keep only those results, as in this case Bob will have made deterministic measurements upon the encoded photons. This is followed by error correction, to remove any errors in their shared key, and privacy amplification to exclude any information known to an eavesdropper. 
       FIG. 2  shows the timing scheme for a prior art quantum cryptographic system. 
       FIG. 2   a  shows the clock signal as a function of time. The clock has a repetition period T clock . The rising edge of the clock signal is used to synchronise Alice&#39;s single photon source  7 , Alice&#39;s phase modulator  23 , Bob&#39;s phase modulator  55  and Bob&#39;s detectors  39 ,  41 . 
     For each clock period, the single photon source is triggered to produce one single photon pulse of width d sps , see  FIG. 2   b .  FIG. 2   b  is a plot of the probability of the output of the single photon source  7  against time. 
       FIG. 2   c  plots the probability of a photon arriving at Bob&#39;s detectors  39 ,  41  (i.e. sum of the probabilities at A  39  and B  41 ) as a function of time. Each single photon pulse now has a width of d bob , which may be greater than d sps  due to dispersion in the fibre. Three arrival windows can be seen for each clock cycle. In order of arrival time, these correspond to photons taking the short-short, long-short or short-long and long-long paths through Alice&#39;s-Bob&#39;s interferometer. Thus the first and second, as well as the second and third pulses are separated by a time delay t delay . 
     Only photons arriving in the central window of each clock cycle undergo interference and are thus of interest. The single photon detectors  39 ,  41  are gated to be on only when the central pulse arrives in each clock cycle, as shown in  FIG. 2   d.    
       FIG. 2   d  is a plot of the gating bias applied to the detector against time. This is achieved by biasing the detector with a voltage V det2  for which it is in an active state for a short duration d det  during each clock cycle when the central pulse arrives. The bias voltage duration d det  is typically chosen to be longer than d bob  and is typically a few nanoseconds. At other times the detector is held at a voltage V det1  for which it is inactive. 
     For a single photon detector based upon an avalanche photodiode, time gating can be achieved by choosing V det2  to be greater than the avalanche breakdown voltage of the diode and V det1  to be less than the breakdown voltage. An avalanche can only be triggered when the diode bias exceeds the breakdown threshold. 
     The avalanche process generates a large number of charge carriers within the diode. Some of these carriers may be localised at hetero-junctions or at trap states within the semiconductor. Carriers confined in such traps can have a lifetime of several microseconds. If the diode is biased above the avalanche breakdown threshold, before the trapped carriers have decayed, there is a possibility that a trapped carrier could be released and then trigger another avalanche. The resultant spurious signal is called an ‘afterpulse’. 
     To minimising the rate of afterpulse counts, the APD has to be biased inactive for a sufficiently long time to allow most of the trapped charge to decay. Thus in a conventional quantum cryptography system, afterpulsing limits the minimum period between APD detection gates and thus the minimum clock period T clock . Typically T clock ˜1 μs. 
     Alice&#39;s and Bob&#39;s phase modulators  23 ,  55  are driven by separate voltage pulse generators. The voltage pulse generators are also synchronised with the clock signal, as shown in  FIG. 2   e .  FIG. 2   e  is a plot of the bias applied to the phase modulator against time. During the pass of each signal pulse through the phase modulator, the pulse generator outputs one of a number of voltage levels, V mod1 , V mod2  etc. For the BB84 protocol, for instance, Alice applied one of four different voltage levels, corresponding to phase shifts of 0°, 90°, 180°, and 270°. Meanwhile Bob applies two voltage levels to his modulator corresponding to phase shifts of 0° and 90°. Alice and Bob vary the applied phase shifts for each signal pulse randomly and independently of one-another. 
       FIG. 3   a  shows an apparatus for quantum cryptography using an unpolarised single photon source in accordance with an embodiment of the present invention. As described in relation to  FIG. 1   a , Alice  101  generates single photons, which she encodes and sends to Bob  103 , along with a bright laser pulse to act as a clock signal. 
     Alice&#39;s equipment  101  comprises a single photon source  107 , a polarising beamsplitter  109 , an early path  111  containing a polarisation rotator  113 , a late path  115  containing a short delay loop  117 , an imbalanced fibre Mach-Zender interferometer  119 , a bright clock laser  121 , a wavelength division multiplexing (WDM) coupler  123  and biasing electronics  125 . The interferometer  119  comprises an entrance fibre coupler  125 , a long arm  127  with a loop of fibre  129  designed to cause an optical delay, a short arm  131  with a phase modulator  133 , and an exit fibre coupler  135 . The bias electronics  125  may comprise a timing unit, a driver for the single photon source  107 , a driver for the clock laser  121  and a driver for the phase modulator  133 . 
     The single photon pulses are generated by a single photon source  107 . Typically each single photon pulse has a duration of d sps =100 ps−1 ns. The single photons are emitted with a random polarisation or a random mixture of two orthogonal polarisations. The present scheme can make use of all the emitted polarisation states. 
     Photons emitted by the single photon source  107  are routed into a polarising beamsplitter  109  which separates the path of photons in two orthogonal polarisations. One of the output arms  111  of the polarising beamsplitter  109  is routed through a polarisation rotator  113 , which rotates the polarisation by 90° and is connected to the second input  137  of Alice&#39;s imbalanced Mach-Zender interferometer  119 . The other output arm  115  of the polarising beamsplitter  109  is routed through a short delay loop  117  and is then fed into the first input  139  of Alice&#39;s imbalanced Mach Zender interferometer  119 . The short delay loop introduces a delay to the photons routed into the first input  139  of Alice&#39;s interferometer  119  of t short  relative to photons routed into the second input  137 . 
     The single photon pulses enter the imbalanced Mach-Zender interferometer  119  through a fibre optical coupler  125 . The long arm  127  of the interferometer  119  contains an optical fibre delay loop  129 , while the short arm  131  contains a fibre optic phase modulator  133 . The length difference between the long arm  127  and the short arm  131  corresponds to an optical propagation delay of t delay . Typically the length of the delay loop  129  may be chosen to produce a delay t delay ˜5 ns. A photon travelling through the long arm  127  will lag that travelling through the short arm  131  by a time of t delay  at the exit of the interferometer  119 . The two arms  127 ,  131  are combined together with a fibre optic coupler  135 . 
     Alice applies a phase delay during the propagation of each signal pulse which is chosen at random from a fixed number of values. For the four-state protocol BB84 described below, for example, the phase delay is either 0°, 90°, 180° or 270°. Alice records the phase modulator  133  setting for each single photon pulse. 
     The output of Alice&#39;s interferometer  119  is multiplexed with the bright clock laser  121  at the WDM coupler  123 . The clock laser  121  may emit at a different wavelength from that of the single photon source  107 , so as to facilitate their easy separation by the receiver Bob  103 . For example the single photon source  107  may operate at 1.3 μm and the clock laser  121  at 1.55 μm or vice versa. 
     The clock  121  may also be delivered in other ways. For example Alice may multiplex the signal pulses with a bright clock laser pulse at the same or different wavelength which is delayed relative to the start of the clock cycle and which does not coincide with the signal pulses. The bright clock pulse may also be prepared in an orthogonal polarisation state to the signal pulses. Alternatively the clock signal may be sent on a separate optical fibre. Alternatively, synchronisation may be achieved by using a timing reference. 
     The multiplexed signal and clock pulses are transmitted to the recipient Bob  103  along an optical fibre link  105 . 
     Bob&#39;s equipment comprises a WDM coupler  151 , a clock recovery unit  153 , a polarisation controller  155 , an imbalanced Mach-Zender interferometer  157 , two single photon detectors  159 ,  161  and biasing electronics  163 . Bob&#39;s interferometer  157  contains an entrance fibre coupler  165 , a long arm  167  having a delay loop  169  and a variable delay line  171 , a short arm  173  having a phase modulator  175 , and an exit fibre coupler  177 . 
     Bob first de-multiplexes the transmitted signal received from fibre  105  using the WDM coupler  151 . The bright clock laser  121  signal is routed to a clock recovery unit  153  to recover the clock signal for Bob to synchronise with Alice. 
     If Alice delivers the clock using an alternative method, Bob will recover the clock accordingly. If Alice sends the clock signal as a single bright pulse within each clock cycle which is delayed relative to signal pulses then Bob may use an imbalanced coupler, such as 90/10, to extract a fraction of the combined signal which is measured with a photo-diode. A clock pulse is then recovered if the incident intensity is above an appropriately set threshold. The efficiency of this scheme may be improved if Alice sends the clock in an orthogonal polarisation state to the signal pulses. Bob then uses a polarisation controller and a polarising beamsplitter to separate the signal and clock pulses. Alternatively Bob may detect the clock on a separate fibre or using a timing reference. 
     The single photon pulses are fed into polarisation controller  155  to restore their original polarisation. 
     The signal pulses then pass Bob&#39;s interferometer  157 . The long arm  167  of Bob&#39;s interferometer  157  contains an optical fibre delay loop  169  and a variable fibre delay line  171 , and the short arm  173  contains a phase modulator  175 . The long arm  167  and the short arm  173  are connected to a 50/50 fibre coupler  177  with a single photon detector  159 ,  161  attached to each output arm. 
     To maximise the interference fringe visibility, the signal pulses at the two input arms of the exit coupler  177  of Bob&#39;s interferometer  157  must be controlled to have same linear polarisation. This can be achieved by using a polarisation controller (not shown) on each of the inputs of the exit coupler  177 . 
     The variable delay line  171  at Bob&#39;s interferometer  157  is adjusted to make the optical delay between its two arms  167 ,  173  similar to that between the arms of Alice&#39;s interferometer  127 ,  131 , t delay . 
     The variable fibre delay line  171  can either be an airgap, or a fibre stretcher, driven by a piezo-electric actuator. Alternatively, the two delays can be balanced by carefully controlling the length of fibre in Alice&#39;s  119  and Bob&#39;s  157  interferometers. Fine adjustment of the length of the two optical paths can be achieved through the calibration of zero phase delay in the two modulators  133 ,  175 . 
     Bob applies a phase delay during the propagation of each signal pulse which is chosen at random from a fixed number of values. For the four-state protocol BB84, for example, the phase delay is either 0° or 90°. Bob chooses the phase delay for each signal pulse randomly and independently of Alice. Bob notes the phase modulator  175  setting for each single photon pulse, as well as the result of the measurement: photon at A  159 , photon at B  161 , no photon detected, or photon at both A  159  and B  161 . 
     There are four possible paths for each signal pulse travelling from Alice&#39;s single photon source to Bob&#39;s single photon detectors:
         i) Alice&#39;s Long Arm  127 -Bob&#39;s Long Arm  167  (Long-Long);   ii) Alice&#39;s Short Arm  131 -Bob&#39;s Long Arm  167  (Short-Long);   iii) Alice&#39;s Long Arm  127 -Bob&#39;s Short Arm  173  (Long-Short); and   iv) Alice&#39;s Short Arm  131 -Bob&#39;s Short arm  173  (Short-Long).       

     The interferometer  157  is balanced so that photons taking paths (ii) and (iii) arrive at nearly the same time within the coherence time of the single photon source at the exit coupler  177  of Bob&#39;s interferometer  157 . Photons taking path (i) have a positive delay t delay , and those taking path (iv) have a negative delay t delay  compared to paths (ii) and (iii). 
     There are 6 different time windows during which a single photon may arrive at Bob&#39;s detector  159 ,  161 , as shown in  FIG. 3   b . Only the photons arriving during the central 2 time windows will undergo interference of paths (ii) and (iii). Thus only these photons are of interest and Bob gates his detectors  159 ,  161  to record only during these central 2 time windows. 
     The delay between signal pulses t short  is chosen to be longer than the response time of the single photon detector  159 ,  161 , so that Bob can distinguish the photons injected into the first input  139  of Alice&#39;s interferometer from those injected into the second input  137 . For an InGaAs APD, for example, the response time is typically ˜200 ps. Typically t short  may be in the range 200 ps-5 ns. Typically t short =2 ns is a convenient value. 
     The length of the delay loops  129 ,  169  in Alice&#39;s and Bob&#39;s interferometer  119 ,  157 , as well as the length of Alice&#39;s short delay loop  117  is carefully selected so that the central arrival window of a photon injected into the first input  139  of Alice&#39;s interferometer will not temporally overlap with a satellite arrival time window of a photon input into the second input  137  of Alice&#39;s interferometer  119  or vice versa. This can be achieved if t delay &gt;t short . For example t delay =5 ns and t short =2 ns. 
     The variable delay is set, and the phase modulators  133 ,  175  calibrated, such that for photons injected into the first input  139  of Alice&#39;s interferometer  133  there is constructive interference at detector A  159  (and thus destructive interference at B  161 ) for zero phase difference between Alice and Bob&#39;s phase modulators  133 ,  175 . 
     By controlling the voltages applied to their phase modulators  133 ,  175 , Alice and Bob determine in tandem whether paths (ii) and (iii) undergo constructive or destructive interference at each detector  159 ,  161 . For the case of zero phase difference between the modulators  133 ,  175 , negligible count rate at detector B  161  for photons injected into the first input  139  to Alice&#39;s interferometer  119  and a finite count rate at detector A  159  is expected. If, on the other hand, the phase difference between Alice and Bob&#39;s modulators  133 ,  175  is 180°, destructive interference at detector A  159  for photons injected into the first input  139  (and thus negligible count rate) and constructive at detector B  161  is expected. For any other phase difference between their two modulators  133 ,  175 , there will be a finite probability that a photon may output at detector A  159  or detector B  161 . 
     Photons injected into the first input  139  of Alice&#39;s interferometer  119  will behave differently to those injected into the second input  137 . This effect is due to the fact that the photons enter the interferometer  119  through different arms of coupler  125 . For instance, if photons injected into the first input  139  of Alice&#39;s interferometer  119  undergo constructive interference at detector A  159  and destructive interference at detector B  161 , the photons injected into the second input  137  will undergo destructive interference at detector A  159  and constructive interference at detector B  161 . Hence it is important that the photons injected into the first  139  and second  137  inputs of Alice&#39;s interferometer can be distinguished temporally. They can then either be modulated differently or the results of Bob&#39;s measurements can be interpreted differently, as described below. The photons injected into the first input  139  of Alice&#39;s interferometer are delayed relative to those input into the second input  137  and arrive at a later time, so that they can be distinguished. 
     Let us firstly consider the case that the results of Bob&#39;s measurements are interpreted differently according to whether the photons are injected into the first or second input port of Alice&#39;s interferometer. This case corresponds to the timing diagrams of  FIGS. 4 and 5 , described below. 
     In the four-state protocol, which is sometimes referred to as BB84, Alice sets the voltage on her phase modulator  133  to one of four different values, corresponding to phase shifts of 0°, 90°, 180°, and 270°. Phase 0° and 180° are associated with bits  0  and  1  in a first encoding basis, while 90° and 270° are associated with 0 and 1 in a second encoding basis. The second encoding basis is chosen to be non-orthogonal to the first. The phase shift is chosen at random for each signal pulse. Alice notes the phase modulator setting for each single photon pulse. 
     Meanwhile Bob randomly varies the voltage applied to his phase modulator  175  between two values corresponding to 0° and 90°. This amounts to selecting between the first and second encoding bases, respectively. Bob records the phase shift applied, whether the photon was recorded in the first or second detection window and the measurement result (i.e detector A  159 , detector B  161  or no photon detected) for each single photon pulse. 
     Bob associates a count in detector A  159  during the second detection window (i.e. for the photons arriving in the later window) with bit=0 and a count in detector B  161  during the second detection window with bit=1. While for the first detection window Bob associates a count in detector A  159  with bit=1 and a count in detector B  161  with bit=0. 
     In the BB84 protocol, Alice  101  and Bob  103  can form a shared key by communicating on a classical channel after Bob&#39;s measurements have taken place. Bob tells Alice in which clock cycle and signal pulse he measured a photon and which measurement basis he used, but not the result of the measurement. Alice then tells Bob the clock cycle and signal pulse in which she used the same encoding basis and they agree to keep only those results, as in this case Bob will have made deterministic measurements upon the encoded photons. Alice and Bob then share a common sifted key, although it may still contain some errors. They can then use classical routines for error correction, to remove any errors in their shared key, and privacy amplification to exclude any information potentially known to an eavesdropper. 
     In the B92 protocol, Alice sets the voltage on her phase modulator  133  to one of two different values, corresponding to phase shifts of 0° or 270°. Alice associates phase 0° with bit  0  and phase 270° with bit  1 . The phase shift is chosen at random for each signal pulse. Alice notes the phase modulator setting for each single photon pulse. Meanwhile Bob randomly varies the voltage applied to his phase modulator  175  between two values corresponding to 180° and 90°. Bob associated a phase shift of 180° with bit  1  and 90° with bit  0 . 
     The phase modulators are calibrated such that when Alice and Bob apply phase shifts of 0° to their modulators, the photon count in detector A  159  will be maximum (and thus it will be minimum in B  161 ) for photons injected into the first input of Alice&#39;s interferometer. Thus, for the photons injected into the first (second) input of Alice&#39;s interferometer, Bob knows that when he records a count in detector A (B), Alice&#39;s phase shift cannot differ from his by 180°. Thus, for the photons injected into the first input of Alice&#39;s interferometer, Bob retains the bit value when there is a count in detector A, as he knows it is the same as that of Alice&#39;s. While, for the photons injected into the second input of Alice&#39;s interferometer, Bob retains the bit value when there is a count in detector B, as again this ensures it is the same as that of Alice&#39;s. To form a shared key Bob tells Alice in which clock cycle he retained the bit value and they agree to keep only those results. Alice and Bob then share a common sifted key, although it may still contain some errors. They can then use classical routines for error correction, to remove any errors in their shared key, and privacy amplification to exclude any information potentially known to an eavesdropper. 
       FIG. 4  shows the timing for a quantum cryptography system with an unpolarised single photon source. 
       FIG. 4   a  shows the clock signal as a function of time. The rising edge of the clock pulses is used to define a reference for each clock cycle. 
     During each clock period T clock , Alice&#39;s single photon source generates a single photon pulse of width d sps . After passing through the short delay loop one of two orthogonal polarisation states generated by the single photon source is delayed by a time t short  relative to the other, as shown in  FIG. 4   b .  FIG. 4   b  is a plot of the probability of a pulse entering Alice&#39;s interferometer  119  as a function of time. 
       FIG. 4   c  plots the probability of a photon arriving at Bob&#39;s detectors (i.e. sum of the probabilities at detector A  159  and detector B  161 ) as a function of time. Each pulse now has a width of d bob , which may be greater than d sps  due to dispersion in the fibre. Photons may arrive in any one of 6 time windows during each clock cycle. The first 2 pulses correspond to photons taking the short arm  131  through Alice&#39;s interferometer  119  and the short arm  173  through Bob&#39;s interferometer  157 . The central 2 pulses correspond to photons taking the short-long or long-short paths (paths (ii) or (iii)). The final 2 pulses correspond to those taking the long-long path (path (i)). 
     Only photons arriving in the central 2 time windows of each clock cycle undergo interference and are thus of interest. The single photon detectors  159 ,  161  are gated to be on only during the central 2 time windows in each clock cycle, as shown in  FIG. 4   d .  FIG. 4   d  is a plot of the detector bias against time. This is achieved by biasing the detector  159 ,  161  with a voltage V det2  for which it is in an active state for N short gates of duration d det  coinciding with the central 2 time windows. At other times the detector  159 ,  161  is held at a voltage V det1  for which it is inactive. The bias duration d det  is chosen to be longer than the width of the arriving pulse d bob . 
     For the case of using an APD as the single photon detector, the APD will be biased above breakdown twice within each clock cycle in close succession. If a photon is detected in the first time window, and thus an avalanche triggered, it is very likely that an afterpulse count will be generated in the second detection window. Thus if a photon is detected during the first detection window, the second detection window is ignored. 
     Alice  101  and Bob&#39;s  103  phase modulators  133 ,  175  are driven by separate voltage pulse generators. The voltage pulse generators are synchronised with the clock signal, as shown in  FIG. 4   e . Explicitly,  FIG. 4   e  is a plot of the phase modulator bias against time. During the pass of each single photon pulse through the phase modulator, the pulse generator outputs one of a number of voltage levels, V mod1 , V mod2  etc, as shown in  FIG. 4   e . For the BB84 protocol, for instance, Alice applied one of four different voltage levels, corresponding to phase shifts of 0°, 90°, 180°, and 270°. Meanwhile Bob applies two voltage levels to his modulator corresponding to phase shifts of 0° and 90°. Alice and Bob vary the applied phase shifts for each signal pulse randomly and independently of one-another. As can be seen in  FIG. 4   e  the same modulation is applied to photons injected into the first and second input of Alice&#39;s interferometer. 
       FIG. 5  shows another scheme for gating the detector. In this scheme, a single gate is applied to the detector during each clock cycle. 
       FIG. 5   a  is a plot of the clock signal against time as per  FIG. 4   a.    
       FIG. 5   b  is a plot of the probability of a photon pulse entering Alice&#39;s interferometer  119  against time as per  FIG. 4   b.    
       FIG. 5   c  is a plot of probability of a photon pulse arriving at either detector  159  and  161  as per  FIG. 4   c.    
       FIG. 5   d  is a plot of the detector bias against time. The single gate has a longer duration d det  than in  FIG. 4   d , so as to detect photons injected into both the first and second input of Alice&#39;s interferometer. The detection time is used to determine to which signal pulse within a clock cycle a detected photon belongs. Only the first detected photon within each clock cycle is retained. 
       FIG. 5   e  is a plot of the bias applied to the modulator as a function of time. 
     The different interference behaviour of photons injected into the two inputs of Alice&#39;s imbalanced interferometer  131  can be compensated by using different driving voltages of either Alice&#39;s  133  or Bob&#39;s phase modulator  175 . One of the two parties, Alice or Bob, modulates the signal pulses from the early input  111  and the late input  177  differently. This is illustrated in  FIG. 6  for the case that Bob modulates photons injected into the two inputs of Alice&#39;s interferometer differently. 
     In the four-state protocol, which is sometimes referred to as BB84, [C H Bennett and G Brassard 1984, in the proceedings of the IEEE International Conference on Computers, Systems and Systems and Signal Processing, Bangalore, India (IEEE, New York), pp 175-179]. Alice still uses 4 different voltages for her phase modulator, and associates 0° and 180° for bits  0  and  1  when encoding the late signal pulse with the first basis, but she associates 180° and 0° for bits  0  and  1  when encoding the early signal pulse. When encoding with second basis, Alice uses 90° and 270° for bits  0  and  1  for the late signal pulse, but 270° and 90° for bits  0  and  1  for the early signal pulse. The bit is chosen random for each single photon pulse, but the encoding the late signal pulse and the early pulse differently. Alice records each bit she used for each clock cycle. 
     Meanwhile Bob randomly varies the voltage applied on his phase modulator  175  between two values corresponding to 0° and 90° phase delay. This amounts to selecting between the first and second measurement bases, respectively. Bob records the phase shift applied and the measurement result. 
     Bob associates a count in detector A  159  with bit=0, and a count in detector B  161  with bit=1 for BOTH photons injected into the first or second input of Alice&#39;s interferometer. In this case, the different interference behaviour of the photons injected into the first and second inputs of Alice&#39;s interferometer is compensated by Alice&#39;s phase modulator. For the same reason, Bob does not need to distinguish counts from the early or late path. 
     The different behaviour between early and late signal pulses can also be compensated by Bob&#39;s phase modulator  175 . Alice&#39;s phase modulator  119  treats the early and late pulses in the same way, but Bob&#39;s phase modulator  175  treats them differently. Bob associates 0° and 90° for the late signal pulse, but 180° and 270° for the early signal pulse. 
     Two-state protocol, often referred as B92 protocol, can also be implemented in such phase-compensated scheme. 
       FIG. 6  shows another timing scheme for a quantum cryptography system with unpolarised single photon source. In this scheme, one of the phase modulators treats the early and late signal pulses differently. 
       FIG. 6   a  is a plot of the clock signal against time as per  FIG. 4   a.    
       FIG. 6   b  is a plot of the probability of a photon pulse entering Alice&#39;s interferometer  119  against time as per  FIG. 4   b.    
       FIG. 6   c  is a plot of probability of a photon pulse arriving at either detector  159  and  161  as per  FIG. 4   c.    
       FIG. 6   d  is a plot of the detector bias against time. The single gate has a longer duration d det  than in  FIG. 4   d , so as to detect photons injected into both the first and second input of Alice&#39;s interferometer. 
     The single photon detectors  159 ,  161  can also be gated to be on only during the two central 2 time windows in each clock cycle, as per  FIG. 4   d.    
       FIG. 6   e  is a plot of the bias applied to one of the two modulators as a function of time. 
       FIG. 6   f  is a plot of the bias applied to the other of the two modulators as a function of time. This phase modulator treats the early and the late signal pulses differently. 
       FIG. 7   a  shows a quantum cryptography system using an unpolarised single photon source and based upon phase encoding in a polarisation sensitive fibre interferometer. 
     Alice&#39;s equipment  201  comprises a single photon source  203 , a polarising beamsplitter  205 , a late path  207  containing a short delay line  209  of polarisation maintaining fibre, an early path  211  containing a polarisation maintaining fibre, an imbalanced fibre Mach-Zender interferometer  215 , a bright clock laser  217 , a wavelength division multiplexing (WDM) coupler  219  and bias electronics  221 . The interferometer  215  comprises of an entrance polarisation maintaining coupler  223 , a long arm - 225  with a loop of fibre  227  designed to cause an optical delay, a short arm  229  with a phase modulator  231 , and an exit polarising beam combiner  233 . All components used in Alice&#39;s interferometer  215  are polarisation maintaining. 
     Single photon pulses are generated by a single photon source  203  with a random polarisation or a random mixture of two orthogonal linear polarisations. 
     The randomly polarised single photon pulses are fed into the polarising beamsplitter  205 . The first output of the polarising beamsplitter  205  is connected to the first input of a polarisation maintaining coupler  223  via a short polarisation maintaining delay loop  207 ,  209  (late path). The second output of the polarising beamsplitter  205  is connected to the second input of a polarisation maintaining coupler  223  through a polarisation maintaining fibre  211  (early path). The late path  207  is longer than the early path  211 , with the effect that photons taking the late path  207  are delayed relative to those taking the early path  211  by a time t short . The two outputs of the polarising beamsplitter  205  are aligned such that the two output polarisations are both coupled into a particular axis, usually the slow axis, of the polarisation maintaining fibre. This ensures that signal pulses taking either the late  207  or early  211  paths will have the same polarisation at the polarisation maintaining coupler  223 . 
     The single photon pulses which now have the same polarisation, are then fed into the imbalanced Mach-Zender interferometer  215  through a polarisation maintaining coupler  223 . The long arm  225  of the interferometer  215  contains an optical fibre delay loop  227 , while the short arm  229  contains a fibre optic phase modulator  231 . The length difference between the long arm  225  and the short arm  229  corresponds to an optical propagation delay of t delay . Typically the length of the delay loop may be chosen to produce a delay t delay ˜5 ns. A photon travelling through the long arm  225  will lag that travelling through the short arm  229  by a time of t delay  at the exit  233  of the interferometer  215 . 
     The long arm  225  and the short arm  229  are combined together with a polarisation beam combiner  233  into a single mode fibre  213 . The fibre inputs of the polarisation beam combiner  233  are aligned in such a way that only photons polarised along a particular axis of the polarisation maintaining fibre, usually the slow axis, are output from the combiner  233 . For example, at the in-line input port  228 , only photons polarised along the slow axis of the in-line input fibre are transmitted by the beamsplitter and pass into the output port and photons polarised along the fast axis are reflected and lost. Meanwhile, at the 90° input port  232 , only photons polarised along the slow axis of the 90° input fibre are reflected by the beamsplitter  233  and pass into the output port, while those polarised along the fast axis will be transmitted and lost. This means that the slow axis of one of the two input fibres is rotated by 90° relative to the output port. Alternatively the polarisation may be rotated using a polarisation rotator before one of the input ports of the polarising beam combiner. Photon pulses that passed through the long  225  and short - 229  arms will have orthogonal linear polarisations when output from the combiner  233 . 
     The single photon pulses are then multiplexed with a bright laser clock source  217  at a different wavelength using a WDM coupler  219 . The multiplexed signal is then transmitted to the receiver Bob  253  along an optical fibre link  251 . 
     The clock may also be delivered in other ways. For example Alice may multiplex the signal pulses with a bright clock laser  217  pulse at the same or different wavelength which is delayed relative to the start of the clock cycle and which does not coincide with the signal pulses. Alternatively the clock signal may be sent on a separate optical fibre. Alternatively, synchronisation may be achieved by using a timing reference. 
     Bob&#39;s setup contains a WDM coupler  255 , a clock recovery unit  257 , a polarisation controller  259 , an imbalanced Mach-Zender interferometer  261 , two single photon detectors  263 ,  265  and biasing electronics  267 . Bob&#39;s interferometer  261  contains an entrance polarising beamsplitter  269 , a long arm  271  containing a delay loop  273  and a variable delay line  275 , a short arm  277  containing a phase modulator  279 , and an exit polarisation maintaining 50/50 fibre coupler  278 . All components in Bob&#39;s interferometer  261  are polarisation maintaining. 
     Bob first de-multiplexes the transmitted signal received from fibre  251  using WDM coupler  255 . The bright clock laser  217  signal is routed to an optical receiver  257  to recover the clock signal for Bob to synchronise with Alice. 
     If Alice delivers the clock using an alternative method, Bob will recover the clock accordingly. If Alice sends the clock signal as a single bright pulse within each clock cycle which is delayed relative to signal pulses then Bob may use an imbalanced coupler, such as 90/10, to extract a fraction of the combined signal which is measured with a photo-diode. A clock pulse is then recovered if the incident intensity is above an appropriately set threshold. Alternatively Bob may detect the clock on a separate fibre or using a timing reference. 
     The single photon pulses are fed into a polarisation controller to restore the original polarisation of the signal pulses. This is done so that signal pulses that travelled the short arm in Alice&#39;s interferometer, will pass the long arm in Bob&#39;s interferometer. Similarly, single photon pulses which travelled the long arm at Alice will travel the short arm at Bob. 
     The single photon pulses then passes Bob&#39;s interferometer  261 . The entrance polarising beamsplitter  269  divides the incident pulses with orthogonal linear polarisation. The two outputs of the entrance polarisation beamsplitter  269  are aligned such that the two output polarisations are both coupled into a particular axis, usually the slow axis, of the polarisation maintaining fibre. This ensures that signal pulses taking either arm will have the same polarisation at the exit 50/50 polarisation maintaining coupler. The long arm  271  of Bob&#39;s interferometer  261  contains an optical fibre delay loop  273  and a variable fibre delay line  275 , and the short arm  277  contains a phase modulator  279 . The two arms  271 ,  277  are connected to a 50/50 polarisation maintaining fibre coupler  278  with a single photon detector A,  263 , B,  265  attached to each output arm. 
     Due to the use of polarising components, there are only two routes for a signal pulse travelling from the entrance of Alice&#39;s interferometer to the exit of Bob&#39;s interferometer:
         (i) Alice&#39;s Long Arm  225 -Bob&#39;s Short Arm  277  and   (ii) Alice&#39;s Short Arm  229 -Bob&#39;s Long Arm  271 .       

     The variable delay line  275  at Bob&#39;s interferometer  261  is adjusted to make the length of routes (i) and (ii) almost equal within the coherence time of the single photon source and thereby ensure interference of the two paths. The variable fibre delay line  275  can either be an airgap, or a fibre stretcher, driven by a piezo-electric actuator. Alternatively, the two delays can be balanced by carefully controlling the length of fibre in Alice&#39;s and Bob&#39;s interferometers. Fine adjustment of the length of the two optical paths can be achieved through the calibration of zero phase delay in the two modulators  231 ,  279 . 
       FIG. 7   b  is a plot of the probability of a photon arriving at either of Bob&#39;s detectors  263 ,  265  against time. Due to the restrictions on the possible paths which photons may take provided by polarisation combiner  233  and polarising beamsplitter  269  only two central peaks are noted. 
       FIG. 8   a  shows a quantum cryptography system using an unpolarised single photon source and based upon phase encoding in a polarisation sensitive fibre interferometer. 
     Alice&#39;s equipment  301  contains a single photon source  303 , a polarising beamsplitter  305 , a late path  307  comprising a short delay line  309  of polarisation maintaining fibre, an early path  311  comprising a polarisation maintaining fibre  311 , a polarising beam combiner  313 , an imbalanced fibre Mach-Zender interferometer  315 , a bright clock laser  317 , a wavelength division multiplexing (WDM) coupler  319  and bias electronics  321 . The interferometer  315  consists of an entrance polarisation maintaining coupler  323 , a long arm  325  with a loop of fibre  327  designed to cause an optical delay, t delay , a short arm  329  with a phase modulator  331 , and an exit fibre coupler  333 . All components used in Alice&#39;s interferometer  315  are polarisation maintaining. 
     Single photon pulses are generated by a single photon source  303  with a random polarisation or a random mixture of two orthogonal linear polarisations. 
     The randomly polarised single photon pulses are fed into the polarising beamsplitter  305 . The first output of the polarising beamsplitter  305  is connected to the first input of a polarising beam combiner  313  via a short polarisation maintaining delay loop  307 ,  309  (late path). The second output of the polarising beamsplitter  305  is connected to the second input of the polarising beam combiner  313  through a polarisation maintaining fibre  311  (early path). The late path  307  is longer than the early path  311 , with the effect that photons taking this path are delayed relative to the other by a time t short . The two outputs of the polarising beamsplitter  305  and the two inputs of the polarising beam combiner  313  are aligned to a particular axis, usually the slow axis, of the polarisation maintaining fibre. Photons taking the two different paths are orthogonally polarised and separated in the clock cycle relative to one another. 
     The late and early signal pulses are fed through the same input arm of the entrance fibre coupler  323  into the imbalanced Mach-Zender interferometer  315 . The long arm  325  contains an optical fibre delay loop  327 , while the short arm  329  contains a fibre optic phase modulator  331 . The length difference between the long arm  325  and the short arm  329  corresponds to an optical propagation delay of t delay . Typically the length of the delay loop  327  is chosen to produce a delay t delay ˜5 ns. A photon travelling through the long arm  325  will lag that travelling through the short arm  329  by a time of t delay  at the exit  333  of the interferometer. The two arms are combined together with a fibre optic coupler  333 . 
     The output of Alice&#39;s interferometer  315  is multiplexed with the bright clock laser  317  at the WDM coupler  319 . The bright clock laser  317  is controlled by biasing electronics  321 . The clock laser  317  may emit at a different wavelength from that of the single photon source  303 , so as to facilitate their easy separation at Bob&#39;s end. For example the single photon source may operate at 1.3 μm and the clock laser at 1.55 μm or vice versa. 
     Bob&#39;s equipment  353  is similar to Alice&#39;s equipment  301  and comprises a WDM coupler  355 , a clock recovery unit  357 , a polarisation controller  359 , an imbalanced Mach-Zender interferometer  361 , two single photon detectors  363 ,  365  and biasing electronics  343 . 
     Bob&#39;s interferometer  361  contains an entrance fibre coupler  369 , a long arm  371  containing a delay loop  373  and a variable delay line  375 , a short arm  377  containing a phase modulator  379 , the long arm  371  and the short arm  377  are combined with an exit 50/50 fibre coupler  378 . 
     Bob first de-multiplexes the transmitted signal received from fibre  351  using WDM coupler  355 . The bright clock laser  317  signal is routed to an optical receiver  357  to recover the clock signal for Bob to synchronise with Alice. 
     If Alice delivers the clock using an alternative method, Bob will recover the clock accordingly. If Alice sends the clock signal as a single bright pulse within each clock cycle which is delayed relative to signal pulses then Bob may use an imbalanced coupler, such as 90/10, to extract a fraction of the combined signal which is measured with a photo-diode. A clock pulse is then recovered if the incident intensity is above an appropriately set threshold. The efficiency of this scheme may be improved if Alice sends the clock in an orthogonal polarisation state to the signal pulses. Bob then uses a polarisation controller and a polarising beamsplitter to separate the signal and clock pulses. Alternatively Bob may detect the clock on a separate fibre or using a timing reference. 
     The single photon pulses are fed into a polarisation controller  359  to restore the original polarisation of the signal pulses. 
     The single photon pulses then passes Bob&#39;s interferometer  361 . The entrance fibre coupler  369  divides the incident pulses. The long arm  371  of Bob&#39;s interferometer  361  contains an optical fibre delay loop  373  and a variable fibre delay line  375 , and the short arm  377  contains a phase modulator  379 . The two arms  371 ,  377  are connected to a 50/50 polarisation maintaining fibre coupler  378  with a single photon detector A,  363 , B,  365  attached to each output arm. 
     There are four routes for a signal pulse travelling from the entrance of Alice&#39;s interferometer to the exit of Bob&#39;s interferometer:
         i. Alice&#39;s Long Arm  325 -Bob&#39;s Long Arm  371     ii. Alice&#39;s Long Arm  325 -Bob&#39;s Short Arm  377     iii. Alice&#39;s Short Arm  329 -Bob&#39;s Long Arm  371     iv. Alice&#39;s Short Arm  329 -Bob&#39;s Short Arm  377         

     The variable delay line  375  at Bob&#39;s interferometer  361  is adjusted to make the length of routes (ii) and (iii) almost equal within the coherence time of the single photon source and thereby ensure interference of paths (ii) and (iii). Photons taking paths (ii) and (iii) arrive at nearly the same time at the exit coupler  378 , corresponding to the central 2 peaks in  FIG. 8   b . Photons taking path (i) have a positive delay t delay  (later arrival time), and those taking path (iv) have a negative delay t delay  compared to paths (ii) and (iii). 
     The variable fibre delay line  375  can either be an airgap, or a fibre stretcher, driven by a piezo-electric actuator. Alternatively, the two delays can be balanced by carefully controlling the length of fibre in Alice&#39;s and Bob&#39;s interferometers. Fine adjustment of the length of the two optical paths can be achieved through the calibration of zero phase delay in the two modulators  315 ,  361 . 
     Only photons arriving in the central windows shown in  FIG. 8   b  undergo interference, and thus are of interest. Bob gates his detectors  363 ,  365  to record only photons in the central windows and not those in the earlier or later satellite windows. 
     The apparatus of  FIG. 8   a  is similar to that of  FIG. 3   a  or  7   a . However, in the apparatus of  FIG. 8   a , the photons generated with the first or second polarisation states are injected into the interferometer with different polarisation, rather than the same polarisation as in the previous examples. It is thus necessary to apply different modulations to the photons generated with the first or second polarisations. 
       FIG. 8   b  is a plot of the probability of a photon arriving at either of Bob&#39;s detectors  363 ,  365  against time. 
       FIG. 9  shows a biasing scheme which is suitable for the apparatus of  FIG. 7   a.    
       FIG. 9   a  is a plot of the clock signal against time as per  FIG. 4   a.    
       FIG. 9   b  is a plot of probability of a photon pulse entering Alice&#39;s interferometer  315  against time as per  FIG. 4   b.    
       FIG. 9   c  is a plot of the probability of a photon arriving at either of Bob&#39;s detectors against time as per  FIG. 4   c.    
       FIG. 9   d  is a plot of the gating bias applied to the detector against time as per  FIG. 5   d.    
       FIG. 9   e  is a plot of the bias applied to the phase modulator against time. It is similar to that in  FIG. 5   e , except that Alice and Bob apply different voltage levels during the times when photons from the early and late paths pass their phase modulators. For example, when photons from early path pass, Alice applies voltages from a set of values V early1 , V early2  etc. When photons from the late path pass, Alice applies voltages from a different set of values V late1 , V late2  etc. In both cases the voltages are chosen to give the desired phase shift for that particular polarisation. Bob will also apply different voltages to the late and early photons, which are not necessarily the same as those applied by Alice. 
     The detector may be gated with one voltage pulse whose duration covers both the early and late photons arrival time (as shown  FIG. 9   d ) or with two separate voltage pulses as per  FIG. 4   d.    
       FIG. 10   a  shows a quantum cryptographic system using an unpolarised single photon source and based upon phase encoding in a polarisation maintaining fibre interferometer. It is similar to that shown in  FIG. 8   a . To avoid unnecessary repetition, same numerals are used for components. 
     As shown in  FIG. 10   a , Alice uses a sufficiently long polarisation maintaining fibre loop  310  to separate in time photons of orthogonal polarisations emitted by the single photon source  303 . Photons polarised along the slow axis of a polarisation maintaining fibre travel in a speed slower than those polarised along the fast axis. Long polarisation maintaining fibre  310  replaces the polarising beamsplitter  305 , the short delay line  309  of polarisation maintaining fibre, the polarisation maintaining fibre  311 , a polarising beam combiner  313  of  FIG. 8   a.    
       FIG. 10   b  is a schematic plot of the probability of a photon being present in a pulse received by a detector against arrival time at the detector. 
       FIG. 11   a  shows an apparatus for quantum cryptography based an unpolarised single photon source and using polarisation encoding. 
     During each clock signal, the single photon source produces one single photon pulse with a random polarisation. 
     Alice&#39;s apparatus  401  comprises a single photon source  403 , a polarising beamsplitter  405 , a polarisation maintaining fibre  407 , a short polarisation maintaining delay loop  409 , a polarising beam combiner  411 , a polarisation encoder  413 , biasing electronics (not shown) and a clock system (not shown). 
     Randomly polarised single photon pulses outputted from the single photon source  403  are fed into the polarising beamsplitter  405 . The first output of the polarising beamsplitter  405  is connected to the first input of a polarising beam combiner  411  via a short polarisation maintaining delay loop  409 . The second output of the polarising beamsplitter  405  is connected to the second input of the polarisation beam combiner  411  through a polarisation maintaining fibre  407 . The path with the short delay loop  409  is longer than that with the polarisation maintaining fibre  407 , with the effect that photons taking this path are delayed relative to the other by a time t short . The polarising beamsplitter  405 , the polarisation beam combiner  411  and the polarisation maintaining fibre  407  and  409  are aligned in such a way that signal has maximal output at the output of the polarisation beam combiner  411 . Signal pulses taking either arm will leave the polarising beam combiner  411  with orthogonal polarisations with a delay of t short  for one of the two polarisations. 
     The single photon pulses are then randomly and individually encoded using a polarisation rotator  413  with variable polarisation rotation. For the BB84 protocol one of four different polarisation rotations is applied: 0°, 45°, 90°, and 135°. Alice associates rotations 0° and 90° with bit=0 and bit=1 in a first encoding basis. Rotations 45° and 135° are associated with bit=0 and bit=1 in a second encoding basis. 
     The encoded photons are then transmitted to the receiver Bob  423  along an optical fibre link  421 . A clock signal may also be sent. 
     Bob  423  first uses a polarisation rotator  425  to recover the original polarisation of the signal pulses. The single photon pulses are either reflected or transmitted by a 50/50 non-polarising beamsplitter  427 . Photons transmitted by the non-polarising beamsplitter  427  are analysed with a polarisation beamsplitter  429  and two single photon detectors A,  431  and B,  433 . Bob associates this with a measurement in the first basis. 
     Bob sets the polarisation controller  429  so that the delayed photons encoded by Alice with a polarisation rotation of 0° produce a maximum count rate in detector A  431  and minimum count rate in B  433 . Bob can then associate a count in detector A  431  as bit=0 and a count in detector B  433  as bit=1 for the delayed photons. For the undelayed photons, Bob associates a count in detector A  431  as bit=1 and a count in B  433  as bit=0. 
     The photons reflected by the non-polarising beamsplitter  427  will first pass through a 45° polarisation rotator  435 , and their polarisation then measured by a polarisating beamsplitter  437  and two single photon detectors C,  439 , D,  441 . Alternatively the polarisation rotator  435  can be omitted and the second polarisation beamsplitter  437  and detectors C,  439 , D,  441  can be rotated by 45°. Bob associates a count in detector C  439  as bit=0 and a count in detector D  441  as bit=1 for the delayed photons. Bob associates this with a measurement in the second basis. For the undelayed photons, Bob associates a count in detector C  439  as bit=1 and a count in D  441  as bit=0. 
     This set-up can be used to implement quantum key distribution using the BB84 in the manner described previously or the B92 protocol [C H Bennett, “Quantum cryptography using any two non-orthogonal states” Phys Rev Lett 68, 3121-3124 (1992)]. 
       FIG. 11   b  is a plot of the probability of a photon arriving at any of detectors A,  431 , B,  433 , C,  439  and D,  441  against time. Two peaks due to photons taking either the early path or the late path are seen. 
     Different polarisation of the early and late signal pulses can be compensated by Alice&#39;s polarisation rotator  413 . The single photon pulses are then randomly and individually encoded using a polarisation rotator  413  with variable polarisation rotation. However the late pulses are modulated differently by the polarisation rotator  413 . For the BB84 protocol one of four different polarisation rotations is applied: 0°, 45°, 90°, and 135° for the early pulses. Since the polarisation of the late pulses is orthogonal to that of the early pulses, we compensate by adding (or subtracting, if appropriate) an extra 90° rotation for the late pulses, so as to make the polarisations of the late and early pulses identical. For BB84 protocol one of the four different polarisation rotations is applied: 90°, 135°, 180° (0°) and 225° (45°). Alice associates rotations 0° and 90° with bit=0 and bit=1 in a first encoding basis for the early pulses, and 90° and 135° with bit=0 and bit=1 in a first encoding basis for the late pulses; Rotations 45° and 135° are associated with bit=0 and bit=1 in a second encoding basis for the early pulses, and rotations 180° (0°) and 225° (45°) are associated with bit=0 and bit=1 in a second encoding basis for the late pulses. 
     The receiver&#39;s apparatus is similar to that described previously. 
     In this case, the orthogonally polarised pulses are modulated differently by encoding means. So, there is no need for Bob&#39;s detector to distinguish photon count from the early path or the late path. 
     It will be apparent to anyone skilled in the art that the B92 protocol may also be applied to this embodiment. 
       FIG. 12   a  is similar to  FIG. 11   a . A polarisation maintaining fibre delay loop is used to delay photons in one of two orthogonal polarisations. 
     During each clock signal, the single photon source produces one single photon pulse with a random polarisation. 
     Alice&#39;s apparatus  501  comprises a single photon source  503 , a polarisation maintaining fibre delay loop  505 , a polarisation encoder  513 , biasing electronics (not shown) and a clock system (not shown). 
     Randomly polarised single photon pulses outputted from the single photon source  503  are fed into the polarisation maintaining fibre delay loop  505 . The polarisation maintaining fibre causes photons having a first polarisation direction to travel down it at one speed and photons having a second polarisation direction to travel down it at a different speed. The fibre may be made long enough so that a clear time gap exists between the photons of the two different polarisations exiting the fibre. 
     The single photon pulses are then randomly and individually encoded using a polarisation rotator  513  with variable polarisation rotation. For the BB84 protocol one of four different polarisation rotations is applied: 0°, 45°, 90°, and 135°. Alice associates rotations 0° and 90° with bit=0 and bit=1 in a first encoding basis. Rotations 45° and 135° are associated with bit=0 and bit=1 in a second encoding basis. 
     The encoded photons are then transmitted to the receiver Bob  523  along an optical fibre link  521 . A clock signal may also be sent. 
     Bob  523  first uses a polarisation controller  525  to recover the original polarisation of the signal pulses. The single photon pulses are either reflected or transmitted by a 50/50 non-polarising beamsplitter  527 . Photons transmitted by the non-polarising beamsplitter  527  are analysed with a polarisation beamsplitter  529  and two single photon detectors A,  531  and B,  533 . Bob associates this with a measurement in the first basis. 
     Bob sets the polarisation controller  529  so that the delayed photons encoded by Alice with a polarisation rotation of 0° produce a maximum count rate in detector A  531  and minimum count rate in B  533 . Bob can then associate a count in detector A  531  as bit=0 and a count in detector B  533  as bit=1 for the delayed photons. For the undelayed photons, Bob associates a count in detector A  531  as bit=1 and a count in B  533  as bit=0. 
     The photons reflected by the non-polarising beamsplitter  527  will first pass through a 45° polarisation rotator  535 , and their polarisation then measured by a polarisating beamsplitter  537  and two single photon detectors C,  539 , D,  541 . Alternatively the polarisation rotator  535  can be omitted and the second polarisation beamsplitter  537  and detectors C,  539 , D,  541  can be rotated by 45°. Bob associates a count in detector C  539  as bit=0 and a count in detector D  541  as bit=1 for the delayed photons. Bob associates this with a measurement in the second basis. For the undelayed photons, Bob associates a count in detector C  539  as bit=1 and a count in D  541  as bit=0. 
     This set-up can be used to implement quantum key distribution using the BB84 in the manner described previously or the B92 protocol [C H Bennett, “Quantum cryptography using any two non-orthogonal states” Phys Rev Lett 68, 3121-3124 (1992)]. 
       FIG. 12   b  is a plot of the probability of a photon arriving at any of detectors A,  531 , B,  533 , C,  539  and D,  541  against time. Two peaks due to photons taking either the early path or the late path are seen. 
       FIG. 13   a  shows an apparatus for outputting polarised single photon pulses. The apparatus comprises an unpolarised single photon emitter  603  driven by either optical or electrical stimulation, a polarisation maintaining fibre delay loop  605 , a polarisation rotator  613 , and biasing electronics (not shown). 
     The single photons emitted from the said single photon source  603  with random polarisations or a random mixture of two orthogonal polarisations. The time duration of such single photon pulse is d sps . The single photons then passed through a polarisation maintaining delay loop  613 . The speed of a photon travelling depends on its polarisation. Photons polarised along the fast axis travels at a faster speed than those polarised along the slow axis of the polarisation maintaining fibre. So, after the polarisation maintaining delay loop  613 , photons of orthogonal polarisations separate in time with a gap t short  and form two pulses, an early pulse and a late pulse. 
     The length of the polarisation maintaining fibre delay loop  613  is selected so that the time gap t short  is larger than the single photon pulse duration d sps , and that the late pulses or the early pulses can be selectively rotated by the polarisation rotator  613 . 
     The polarisation rotator  613  is synchronised with the single photon emitter  603 . The rotator only rotate polarisation of one of the pulses, either the early or late pulse within each clock cycle, by 90°. In this way, the early signal pulses and the late signal pulses will have same polarisation after the polarisation rotator  613 . 
       FIG. 13   b  to  13   e  shows how devices are timed. 
       FIG. 13   b  is a plot of the clock signal against time. 
       FIG. 13   c  is a plot of the probability of a photon pulse entering the polarisation maintaining delay loop  605  as a function of time. Here, the photon pulse is not polarised. 
       FIG. 13   d  is a plot of the probability of a photon pulse leaving the polarisation maintaining delay loop  605  as a function of time. Since photons of orthogonal linear polarisation travel at different speed, vertically polarised and horizontally polarised photons are separated in time by a gap t short . There are two time windows when a photon may leave the delay loop. The early and the late pulses are orthogonally linearly polarised. 
       FIG. 13   e  is a plot of the bias applied on the polarisation rotator as a function of time. 
       FIG. 13   f  is a plot of the probability of a photon pulse leaving the polarisation rotator  613  as a function of time. Note that the early and late pulses now have same linear polarisation. 
       FIG. 14  shows an apparatus for outputting polarised single photon pulses. The apparatus comprises an unpolarised single photon emitter  703  driven by either optical or electrical stimulation, a polarising beam splitter  705 , a polarisation maintaining fibre delay loop  709 , a short polarisation maintaining fibre link  707 , a polarising beam combiner  711 , and a polarisation rotator  713 . 
     Single photon pulses are generated by a single photon source  703  with a random polarisation or a random mixture of two orthogonal linear polarisations. 
     The randomly polarised single photon pulses are fed into the polarising beamsplitter  705 . The first output of the polarising beamsplitter  705  is connected to the first input of a polarising beam combiner  711  via a polarisation maintaining delay loop  709  (late path). The second output of the polarising beamsplitter  705  is connected to the second input of the polarising beam combiner  711  through a polarisation maintaining fibre  707  (early path). The late path  709  is longer than the early path  707 , with the effect that photons taking this path are delayed relative to the other by a time t short . The two outputs of the polarising beamsplitter  305  and the two inputs of the polarising beam combiner  711  are aligned to a particular axis, usually the slow axis, of the polarisation maintaining fibre. Photons taking the two different paths are orthogonally polarised and separated in the clock cycle relative to one another when leaving the polarising beam combiner  711 . 
     The length of the polarisation maintaining fibre delay loop  709  is selected so that the time gap t short  is larger than the single photon pulse duration d sps , and that the late pulses or the early pulses can be selectively rotated by the polarisation rotator  613 . 
     After passing the polarisation beam combiner  711 , there are two time windows (early and late) in which a single photon may exist. Photons within different widows will have orthogonal linear polarisations. 
     The polarisation rotator  713  is synchronised with the single photon emitter, and it is gated on only to rotate the polarisation of later pulses by 90°. In this way, a single photon leaving the polarisation rotator  713  will have fixed linear polarisation, which is independent of its original polarisation. 
       FIG. 14  is similar to  FIG. 13   a . The only difference is that means with polarisation splitting and combining are used to separate photons of orthogonal polarisations in time in  FIG. 14 , while in  FIG. 13   a  photons are separated by their different travelling speed in a polarisation maintaining fibre loop.