Abstract:
With the object of providing a practical quantum circuit capable of discriminating Bell states in order to realize transmission of quantum states with high fidelity, a quantum circuit comprises: a two-photon absorbing crystal that selectively absorbs, in accordance with known selection rules, a photon pair of a Bell state that is determined depending on crystal symmetry of said two-photon absorbing crystal; a two-photon absorption detector that detects absorption of photon pairs by said two-photon absorbing crystal; and a polarization element that converts the Bell state of a polarized photon pair. The two-photon absorbing crystal makes two-photon absorption of a photon pair of a specific Bell state only. Electrons that have been excited by the two-photon absorption are detected by the detector.

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to quantum communication and a quantum computer that employs light, and more particularly to a quantum circuit that effects measurements of quantum states. 
     The explosive increase in widespread use of the Internet and the practicability of electronic commerce transactions have increased the social needs for encryption technology, which includes maintenance of confidentiality of communications, prevention of forgery, and user authentication. At present, common key methods such as DES (Data Encryption Standard) codes and public key methods including RAS (Rivest, Shamir, Adleman Public Key Encryption) codes are in wide use. However, these methods are based on “safety through computational load,” and current encryption methods are therefore always threatened by progress in computer hardware and code decryption algorithms. 
     The laws of physics, in contrast, guarantee the safety of “physical codes” such as quantum codes, and these physical codes therefore can guarantee ultimate safety that does not depend on limitations of the capabilities of computers. Putting such an encryption method into practical use would have an extremely powerful social impact, and such encryption methods are expected to become one of the technological foundations of the information industry in the future. 
     The transmission of quantum information, of which quantum code is representative, is limited to a distance of several tens of kilometers due to loss and disturbance of the quanta (photons) that are used in transmission. In addition, intercommunication is limited to the two ends of the optical fiber that makes the transmission path, and quantum communication with multiple partners therefore requires the establishment of a large number of optical fibers. To solve these problems and realize quantum networking that can implement quantum information communication over a wide range requires technology such as relays and exchanges. Of course, relays and exchanges can be realized by converting quantum information to classical information at a relay station, but such a solution would interrupt the advantageous properties inherent in quantum information communication. In a case in which quantum encryption keys are distributed, for example, a wire-tapper could obtain access to all information by breaking into a relay station, and the safety against wiretapping that is the advantage of quantum information would be lost. 
     For these reasons, there is a need for quantum relays and quantum exchanges that relay and exchange quantum information as is. Quantum relays and quantum exchanges are also vital for distributed quantum computers. The utilization of quantum teleportation by a quantum relay can realize various effects as described hereinbelow. Quantum information is carried by entangled photon pairs that imply quantum correlation and by classical information separately. When entanglement swapping is used, transmission can be implemented by swapping entangled photon pairs at successive repeaters. The sender provides the swap information to the receiver as classical information. 
     By means of this entanglement swapping method, the receiver and sender can share entangled photon pairs even when separated by great distances. 
     Quantum teleportation and entanglement swapping are predicated on the generation of entangled photon pairs and the measurement of Bell states. In Bell-state measurement, two photons are discriminated to be in one of four entangled states, referred to as Bell states. Although the principles of quantum teleportation and entanglement swapping have been confirmed through experimentation, it is not possible with the currently available technology to discriminate all of four Bell states, and transmission by any desired quantum state is therefore yet to be realized. 
     In Science, 282, 706 (1998), Furusawa, A. et al. reported on quantum teleportation that does not require measurement of Bell states. Although this method enables transmission in any quantum state, it entails 100% squeezing of light. However, due to the insufficient squeezing of the light source that is currently obtainable, the obtainable fidelity of the transmitted quantum states is no higher than 58%. Nevertheless, a fidelity of nearly 100% can be expected if Bell-state measurement can be realized. 
     For the measurement of Bell states, methods are normally adopted that employ detection circuits composed of photon detectors and linear-optical elements such as semitransparent mirrors and polarization beam splitters. However, such methods can discriminate only two of the four Bell states. 
     The Bell state of two photons can be represented in the framework of concept of the linear-optics by the following equations: 
     
       
         Φ(±)=(| x&gt;|x&gt;±|y&gt;|y &gt;)/2 ½   (1) 
       
     
     
       
         Ψ(±)=(| x&gt;|y&gt;±|y&gt;|x&gt;)/ 2 ½   (2) 
       
     
     where |x&gt; and |y&gt; are the state functions for photons polarized in the directions of the x-axis and the y-axis, respectively. 
     As can be understood from equations (1) and (2), a Bell state is a superposed state of a two-photon state specified by a set of two directions of polarization and the state specified by the exchanged directions of polarization of two photons. Φ(±) are states in which the two photons polarize in the same direction, the state being symmetrical (+) or antisymmetrical (−) with respect to exchange of the directions of polarization; and Ψ(±) are states in which the two photons polarize in orthogonal directions, the state being symmetrical (+) or antisymmetrical (−) with respect to the exchange of the direction of polarization. 
     FIG. 1 shows the configuration of an example of a Bell-state measurement circuit of the prior art that employs linear-optical elements. 
     The Bell-state measurement circuit is constituted by linear-optical elements including semitransparent mirror  51  and polarization beam splitters  52  and  53 , and photon detectors  54 ,  55 ,  56 , and  57 . Polarization beam splitters  52  and  53  split incident polarized light into s-polarized light that oscillates in a direction perpendicular to the plane of incidence, and p-polarized light that oscillates within the plane of incidence. Photon detectors  54  and  55  detect s-polarized light and p-polarized light, respectively, emerging from polarization beam splitter  52 . Photon detectors  56  and  57  detect the s-polarized light and p-polarized light, respectively, emerging from polarization beam splitter  53 . 
     Polarized light of one of the four Bell states is incident on this Bell-state measurement circuit. The possible Bell states obtained from the response of photon detectors  54 - 57  are shown in Table 1. 
     As can be seen from Table 1, the Bell-state measurement circuit realized by the linear-optical elements shown in FIG. 1 can discriminate the Ψ(±) states but cannot discriminate one of the Φ(±) states. Although it is known that the use of a quantum gate, referred to as a light-controlled NOT gate, enables all four Bell states to be discriminated, a practically realizable device of this type of quantum gate has still not been known. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 detector that detects a photon 
                 possible Bell state 
               
               
                   
                   
               
             
             
               
                   
                 54 and 55 
                 Ψ (+) 
               
               
                   
                 54 and 57 
                 Ψ (−) 
               
               
                   
                 55 and 56 
                 Ψ (−) 
               
               
                   
                 56 and 57 
                 Ψ (+) 
               
               
                   
                 any one of 54-57 
                 Φ (±) 
               
               
                   
                   
               
             
          
         
       
     
     Scully M. O. et al. have recently proposed in Physical Review Letters 83, 4433 (1999) a method of measuring Bell states that employs two-photon absorption. In this method, the Bell states are specified in terms of circularly polarized light, the light is passed through three atomic cells to cause two-photon absorption, and the fluorescence emitted from the atomic cell caused by two-photon absorption is observed. The absorption of only one specific Bell state can be caused if the atoms in the cells are prepared in advance by a strong electromagnetic field such that the atomic wave function is represented in a special superposition of unperturbed atomic wave functions. The Bell state of the incident light can thus be determined by observing which cells absorb light. If two-photon absorption does not occur in any of the three cells, it can be concluded that the incident light was in the remaining one Bell state. 
     The two-photon absorption in the method of Scully et al. uses atoms that have been prepared in advance by a strong electromagnetic field such that their wave function has a specific superposed state. However, it is difficult to keep the state of the atoms in the prepared state in which a plurality of states are superposed. Moreover, the method of Scully et al. necessitates three cells containing the atoms that have been thus prepared. Furthermore, since the atoms are contained in the cells as a gas, the atoms have a low density and the probability of two-photon absorption is low. To obtain two-photon absorption with sufficiently high probability, the cells must be extremely long, and this renders the method impractical. Still further, since the probability of observing fluorescence from electrons that have been excited by two-photon absorption is also not high, there is a high probability of error in discriminating the Bell states when fluorescence can not be observed. Transmission of quantum states cannot be achieved with high fidelity if errors occur in discriminating the Bell states. 
     It is a principal object of the present invention to provide a practical quantum circuit capable of measuring Bell states using a material that absorbs photon pairs with sufficiently high probability and that does not require setup of atomic states by means of an external electromagnetic field in order to realize communication of quantum states with high fidelity. 
     SUMMARY OF THE INVENTION 
     The quantum circuit of the present invention is provided with: a two-photon absorbing crystal having the crystal symmetry selected so that the two-photon absorbing crystal selectively absorbs a photon pair of a prescribed Bell state in accordance with selection rules based on crystal symmetry; and a two-photon absorption detector that detects absorption of photon pairs by said two-photon absorbing crystal. 
     The quantum state of an incident optical signal is a state in which four Bell states are superposed or entangled and it is intended that one of the entangled four Bell states is discriminated by means of the two-photon absorption by the crystal having a crystal symmetry that permits two-photon absorption of a polarized photon pair in the Bell state to be discriminated. 
     If the two-photon absorbing crystal has crystal symmetry that permits two-photon absorption of a polarized photon pair in any one of a plurality of Bell states that correspond to degenerated final states of exciton production in said two-photon absorbing crystal, a perturbation field is applied to said crystal so that the two-photon absorbing crystal will selectively absorb the polarized photon pair in only one of the plurality of the Bell states. 
     Electrons that are excited by two-photon absorption are detected by the two-photon absorption detector. The use of polarization elements enables the one-to-one conversion of one Bell state to another Bell state. All of the Bell states can be discriminated by successively repeating the operations of: converting the Bell state of a photon pair that have been transmitted by a two-photon absorbing crystal, to another Bell state; directing this photon pair to another two-photon absorbing crystal; and detecting. 
     The quantum states of polarized light include the four Bell states Φ(+), Φ(−), Ψ(+), and Ψ(−). 
     Φ(+) is a state in which the directions of polarization of the photon pair are the same and that is symmetrical with respect to the exchange of the directions of polarization; Φ(−) is a state in which the directions of polarization of the photon pair are the same and that is antisymmetrical with respect to t he exchange of the directions of polarization; Ψ(+) is a state in which the directions of polarization of the photon pair are orthogonal and that is symmetrical with respect to the exchange of the directions of polarization; and Ψ(−) is a state in which the directions of polarization of the photon pair are orthogonal and that is antisymmetrical with respect to the exchange of the directions of polarization. 
     The above-described quantum circuit requires four two-photon absorbing crystals to discriminate the four Bell states Φ(+), Φ(−) Ψ(+) and Ψ(−). However, since two states Ψ(+) and Ψ(−) can be discriminated by using a prior-art quantum circuit as shown in FIG. 1 using linear-optical elements, it suffices for the Φ(+) state and Φ(−) state ( which cannot be discriminated by linear-optical elements), to be absorbed by two-photon absorbing crystals and detected, and for the remaining Ψ(+) and Ψ(−) states to be discriminated by linear-optical elements. 
     The quantum circuit to discriminate two Bell states such as Φ(+) and Φ(−) states is constituted by: a first two-photon absorbing crystal having the crystal symmetry selected so that the two-photon absorbing crystal selectively absorbs a photon pair of a first prescribed Bell state in accordance with selection rules based on crystal symmetry; a first two-photon absorption detector that detects absorption of photon pairs by the two-photon absorbing crystal; a second two-photon absorbing crystal having the crystal symmetry selected so that the two-photon absorbing crystal selectively absorbs a photon pair of a second prescribed Bell state in accordance with selection rules based on crystal symmetry; a second two-photon absorption detector for detecting the absorption of photon pairs by said second two-photon absorbing crystal; and a first polarization element that converts a first transmitted Bell state to the second prescribed Bell state. 
     Here the first transmitted Bell state is one of the possible Bell states of a polarized photon pair that have been transmitted by said first two-photon absorbing crystal. 
     As an embodiment of this quantum circuit, if the first and second two-photon absorbing crystals are both crystals that absorb the Φ(+) Bell state, the above-described first and second prescribed Bell states are both Φ(+). Then, if the first transmitted Bell state is Φ(−), a polarization element that converts Bell state Φ(−) to Bell state Φ(+) is used as the first polarization element. In this case, the first polarization element can be a retarder means that provides a 90° phase difference between the oscillations in polarization directions of each photon of the photon pair. 
     In this way, the discrimination of Bell states Φ(+) and Φ(−) from the incident polarized light is enabled. 
     As the polarization element, a retarder can be used that provides a 90° phase difference between the oscillations in polarization directions of each photon of the photon pair when converting from Bell state Φ(±) to Bell state Φ(∓) Conversion from Bell state Φ(±) to Bell state Ψ(∓) can also be realized by arranging an optical rotator of 90° rotation in one of the photon paths. The conversion from Ψ(±) to Ψ(∓) is achieved by retarders for providing a 90° phase difference between the oscillations in polarization directions of one of the photon pair and a −90° phase difference to the oscillations of the other photon. 
     Generally, the absorption of photons of Bell state Φ(−) is weaker than the absorption of photons of Bell state Φ(+), and the absorption of photons of Bell state Ψ(−) is weaker than the absorption of photons of Bell state Ψ(+). As a result, a crystal having a crystal symmetry that absorbs photons having Bell state Φ(+) or photons having Bell state Ψ(+) is used as the two-photon absorbing crystal. 
     Accordingly, polarization elements are also used that convert to Bell state Φ(+) or to Bell state Ψ(+). 
     According to the present invention, each of the four Bell states is discriminated by a different discrimination means, and as a result, even in the event of discrimination failures, the possibility of discriminating an incorrect Bell state is limited to failures caused by noise of the detectors and is therefore small. Bell-state discrimination can therefore be realized with a low level of error. 
     The discrimination of all Bell states in the present invention is thus realized by the discrimination of specific Bell states by quantum interference and polarization selection rules of two-photon absorption that are based on the symmetry of a crystal and by the conversion of Bell states by polarization elements; and there is consequently no need for preparations in advance such that the wave functions of an atom are employed with particular superposition. 
     In addition, strong two-photon absorption can be expected because a solid is used. As a result, a practical quantum circuit can be realized that can absorb photon pairs with sufficiently high probability and discriminate Bell states using a material that does not require the preparation of the state of an atom by an external electromagnetic field. 
     Although extremely rapid phase relaxation is normally a problem in quantum circuits that employ a solid material, the effect of phase relaxation is not a problem in the present invention because electrons that have been excited by two-photon absorption need not maintain coherence. 
     The above and other objects, features, and advantages of the present invention will become apparent from the following description referring to the accompanying drawings which illustrate examples of preferred embodiments of the present invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a structural view of a Bell-state measurement circuit of prior art; 
     FIG. 2 is a structural view of a quantum circuit showing the first embodiment of the present invention; 
     FIG. 3 shows Clebsch-Gordan coefficients for two-photon absorption; 
     FIG. 4 is a structural view of a quantum circuit showing the second embodiment of the present invention; 
     FIG. 5 is a structural view of a quantum circuit showing the third embodiment of the present invention; 
     FIG. 6 is a structural view of a quantum circuit showing the fourth embodiment of the present invention; and 
     FIG. 7 is a structural view of one example of the resonator with inserted two-photon absorbing crystal. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Embodiments of the present invention are next explained with reference to the accompanying drawings. 
     FIG. 2 is a structural view of the first embodiment of a quantum circuit of the present invention. 
     The quantum circuit of this embodiment is provided with Bell-state discrimination circuit (BSDC)  101  and Bell-state measurement circuit (BSMC)  15 . Bell-state discrimination circuit  101  is provided with: two-photon absorbing crystal (TPAC)  11 , photoelectricity detector (PD)  16 , retarders (RTD)  13  and  14 , two-photon absorbing crystal  12 , photoelectricity detector  17  (PD), and reflecting mirrors. The reflecting mirrors are used to deflect light beams in the direction of the optical axes of the optical system constituted by two-photon absorbing crystal  11 , retarders  13  and  14 , and two-photon absorbing crystal  12 . 
     Two-photon absorbing crystals  11  and  12  employed in this embodiment are cubic crystals such as cuprous chloride (CuCl), which absorb photon pairs and generate exciton molecules inside the crystal. The exiton molecule is a hydrogen molecule-like compound of two excitons. The crystal thereby changes in electrical conductivity. Photoelectricity detectors  16  and  17  then detect change in the electric conductivity of two-photon absorbing crystals  11  and  12 , respectively, and thus detect the occurrence of two-photon absorption from these detection results. 
     As Bell-state measurement circuit  15  in this embodiment, the circuit of the prior art is employed that was explained with reference to FIG.  1 . 
     Retarders  13  and  14  have their principal axes directed in the x and y directions, respectively, and provide a 90° phase difference to oscillations in the directions of the two principal axes. In this way, each retarder provides a 90° phase difference between the oscillations in polarization directions of each photon of the photon pair. 
     Incident light is set to resonate with two-photon absorption that causes generation of exciton molecules. Incident light is further set to be substantially perpendicular to the crystal surface (a perpendicular incidence). It is assumed in the preferred embodiments described in this Specification that the direction of incidence is directed substantially to the z-axis. 
     Polarized light in an entangled Bell state is incident on two-photon absorbing crystal  11 . Light transmitted by two-photon absorbing crystal  11  passes through retarders  13  and  14 , and a 90° phase difference is caused in oscillation in the directions of two principal axes, i.e., the x and y directions. The light is then directed into two-photon absorbing crystal  12 , which has the same crystal structure as crystal  11 . The photon state of light that has been transmitted by two-photon absorbing crystal  12  is discriminated by Bell-state measurement circuit  15  constituted by linear-optical elements. 
     The exciton molecules created by two-photon absorption are thermally ionized at room temperature. The electric currents caused by the ionization are detected as photoelectric signals by photoelectricity detectors  16  and  17 . 
     The exciton molecule created in a cubic crystal such as cuprous chloride (CuCl) has a total symmetry (Γ1), and as a result, the incidence of two linearly-polarized photons results in two-photon absorption when the directions of polarization of the incident polarized photons are parallel. Accordingly, the photon pair must be in the |x&gt;|x&gt; state or the |y&gt;|y&gt; state in order for two-photon absorption to occur. Of the Bell states, two-photon absorption does not occur in the Ψ(±) states in which the two photons have differing directions of polarization. 
     When a photon pair of the Φ(+) state is incident, absorption resulting from |x&gt;|x&gt; and |y&gt;|y&gt; reinforce each other, but when the Φ(−) state is incident, absorption caused by |x&gt;|x&gt; and |y&gt;|y&gt; cancel each other through quantum interference. As a result, only the Φ(+) state is detected through two-photon absorption by the two-photon absorbing crystal employed in this embodiment. A photon pair of the Φ(−) state transmitted through two-photon absorbing crystal  11  are converted to the Φ(+) by retarders  13  and  14 , while the Ψ(±) states remain unconverted. 
     When the outputs of retarders  13  and  14  are incident on two-photon absorbing crystal  12  having the same crystal structure as crystal  11 , the Bell component Φ(+) that has been converted from the Φ(−) state experiences two-photon absorption. As a result, light that has not been absorbed by two-photon absorbing crystal  12  is only the light in the Ψ(±) states. Polarized light in the Ψ(±) states is discriminated by Bell-state measurement circuit  15  described above. Thus, all four of the Bell states can be detected by the procedures described hereinabove. 
     As the final state of two-photon absorption in a crystal having cubic symmetry, the possible electron states include states having Γ3 and Γ5 symmetries in addition to the state of total symmetry Γ1. These states are electron states of exciton molecules in a crystal such that the symmetry of the wave function of electrons occupying the highest energy level in the valence band is Γ8, as is the case with copper bromide (CuBr). In addition, the electron state of an exciton (an exciton that exists singly without forming an exciton molecule) that is created in a crystal having cubic symmetry have Γ5 symmetry. The polarization selection rule of two-photon absorption can be known from the Clebsch-Gordan coefficients shown in FIG.  3 . 
     In FIG. 3, the notation Γ3 for example denotes the symmetry of the eigenfunction of the final state in two-photon absorption. The notation xy is the probability amplitude or eigenfunction of an exciton molecule created through x- and y-polarized two photon absorption. 
     In FIG. 3, only the superposition (quantum interference) of the polarized photons corresponding to coefficients of not 0 contributes to two-photon absorption. If the signs of the coefficients are the same, the Bell state that is symmetrical with respect to exchange of polarization directions undergoes two-photon absorption. If the signs of the coefficients are opposite, the Bell state that is antisymmetrical with respect to exchange of the polarization directions undergoes two-photon absorption. 
     FIG. 4 is a block diagram showing the configuration of the second embodiment of the present invention. Referring to FIG. 4, elements identified by the same reference numerals as FIG. 2 are elements having the same function as the corresponding elements in FIG.  2 . 
     In the case that an employed crystal has crystal symmetry in which the final state of two-photon absorption has Γ 3  symmetry, it is not necessarily required to use polarization elements such as retarders to alter the Bell state. FIG. 4 shows a quantum circuit for such a case. 
     The two degenerated state of exciton molecules having Γ3 symmetry can be split into two non-degenerated states by applying uniaxial stress to the two-photon absorbing crystal or by forming a quantum well in the two-photon absorbing crystal. 
     As can be understood from FIG. 3, one of the states having Γ3 symmetry (the upper row of Γ3 state in FIG. 3) is a final state created through absorption of two photons in the Φ(+) state, and the other state (the lower row Γ3 state in FIG. 3) is a final state created through absorption of two photons in the Φ(−) state. 
     Although these two states have equal energy (energy degeneration), applying a perturbation field of tetragonal symmetry such as a quantum well to lower the crystal symmetry can separate their energy level. 
     Alternatively, only one of the two degenerated states can be set to resonate with the two-photon absorption of incident light by, for example, applying an electric field to the two-photon absorbing crystal. Thus, instead of using retarders in this embodiment, power supply (PS)  21  is provided to apply an electric field to each of the two-photon absorbing crystals to separate the degenerated energy levels of the exciton molecule. 
     By preparing a crystal so that degenerated energy levels of exciton molecule states are separated so as to have one of the states resonate with two-photon absorption, and by using two crystals prepared in this manner, absorption of two photons either in the Φ(+) state or in the Φ(−) state can be made by each of the two crystals. 
     Next, FIG. 5 shows a block diagram of a third embodiment of the present invention illustrating a configuration of a quantum circuit. 
     In this embodiment, the two-photon absorbing crystal has crystal symmetry in which the final state of two-photon absorption has the Γ5 symmetry. Optical rotator (OR)  31  for rotating polarized light 90° is inserted in one of the optical paths before incidence to two-photon absorbing crystal  11 . 
     One of the light beams transmitted by two-photon absorbing crystal  11  passes through retarder  13 , which provides a 90° phase difference to oscillations in the directions of the two principal axes; and the other beam of light passes through retarder  14 , which provides a −90° phase difference to oscillations in the direction of the two principal axes. In this embodiment, the two principal axes are directed to the x and y directions. 
     Light that has passed through retarders  13  and  14  then passes through two-photon absorbing crystal  12 , which has the same crystal structure as two-photon absorbing crystal  11 . Optical rotator  32  for rotating polarized light −90° is inserted in one of the optical paths of light that has passed through two-photon absorbing crystal  12 . The state of the photons is then discriminated by Bell-state measurement circuit (BSMC)  15 , which is constituted by linear-optical elements 
     When the final state of two-photon absorption has Γ5 symmetry, only the Ψ(+) state is selected for two-photon absorption (see the third row of Γ5 symmetry in FIG.  3 ). Of the Bell states, optical rotator  31  converts the Φ(−) state to the Ψ(+) state. At this time, the Φ(+) state is converted to the Ψ(−) state, and the Ψ(±) states are converted to the Φ(∓), respectively. 
     When light of these Bell states is incident to two-photon absorbing crystal  11 , only light that has been converted from the Φ(−) state to the Ψ(+) state is absorbed through two-photon absorption. In this way, of the Bell states of the incident polarized light, the Φ(−) state is first detected. 
     The Ψ(−) state is next converted to the Ψ(+) state by retarders  13  and  14 , but the Φ(±) states are not converted by retarders  13  and  14 . Accordingly, only photons currently in the Ψ(+) state (light that was in the Φ(+) state before incidence to optical rotator  31 ) undergo two-photon absorption in two-photon absorbing crystal  12 . Thus, of the Bell states of the incident polarized light, the Φ(+) state is detected by two-photon absorbing crystal  12 . 
     The Bell state that has been converted to the Φ(∓) states by optical rotator  31  is then returned to the original Ψ(+) states by optical rotator  32 . These Ψ(±) states are discriminated by Bell-state measurement circuit (BSMC)  15 , which is constituted by linear-optical elements. 
     In FIG. 5, as in FIG. 4, retarders  13  and  14  can be omitted by making two-photon absorbing crystal  11  absorb Φ(+) photon pairs and two-photon absorbing crystal  12  absorb Φ(−) photon pairs. 
     Next, a fourth embodiment of the present invention will be explained. 
     Although, in the previously described circuit, the Ψ(±) states were discriminated by Bell-state measurement circuit  15  which is constituted by linear-optical elements, it is also possible to convert the Bell states Ψ(±) by means of retarders or optical rotators and detect all four Bell states by two-photon absorbing crystals. 
     FIG. 6 shows the configuration of an embodiment of a quantum circuit when using crystals having crystal symmetry in which the final state of two-photon absorption has Γ1 symmetry. 
     In the quantum circuit of this embodiment, a configuration is adopted in which two Bell-state discrimination circuits (BSDC)  104  and  105  having the same arrangement as Bell-state discrimination circuit  101  of the first embodiment are arranged in series with optical axes aligned on a single line and optical rotator  31  inserted between the two discrimination circuits  104  and  105 . 
     Bell-state discrimination circuit  104  detects Bell states Φ(+) and Φ(−), similarly to Bell-state discrimination circuit  101  of the first embodiment. 
     Bell-state discrimination circuit  105 , however, together with preposed optical rotator  31  , detects Ψ(+) and Ψ(−) as described hereinbelow. 
     Optical rotator  31 , which is inserted in one of the optical paths of light transmitted by two-photon absorbing crystal  12 , rotates polarized light 90°. Bell states Ψ(+) and Ψ(−) are consequently converted to Bell states Φ(−) and Φ(+), respectively. When photon pairs entangled with these Bell states are incident to two-photon absorbing crystal  41 , only the Φ(+) state experiences two-photon absorption. Since this Φ(+) state was originally (when incident to Bell-state discrimination circuit  104 ) Bell state Ψ(−), the Ψ(−) state is discriminated by detecting the photoelectricity conductivity of two-photon absorbing crystal  41 . 
     A photon pair of the Φ(−) state that have been transmitted by two-photon absorbing crystal  41  pass through retarders  43  and  44  and are converted to Bell state Φ(+) The retarders give a 90° phase difference to oscillations in the directions of the two principal axes, as described above. In this embodiment, the principal axes are directed to the x and y directions. 
     This polarized light of Bell state Φ(+) is incident to two-photon absorbing crystal  42  and absorbed. 
     In this way, the original Ψ(+) Bell state is discriminated by detecting the photoelectricity conductivity of two-photon absorbing crystal  42 . 
     Each of the different Bell states is thus discriminated by four two-photon absorbing crystals  11 ,  12 ,  41 , and  42 . 
     Although the embodiment of FIG. 6 is an example in which Ad the final-state symmetry is Γ1, all Bell states can be similarly detected in cases in which the final state has different symmetry. 
     Although Bell-state discrimination circuits  104  and  105  in FIG. 6 are identical to Bell-state discrimination circuit  101  of FIG. 2, these circuits may be replaced by Bell-state discrimination circuit  102  of FIG. 4 or Bell-state discrimination circuit  103  of FIG.  5 . In a case in which Bell-state discrimination circuits  104  and  105  are replaced with Bell-state discrimination circuit  102  of FIG. 4, retarders  13  and  14  can be omitted by the same method as the quantum circuit of FIG. 4 in which two-photon absorbing crystal  11  absorbs photon pairs of the Φ(+) state and two-photon absorbing crystal  12  absorbs photon pairs of the Φ(−) state. 
     Although two-photon absorbing crystals in the foregoing explanation are cubic crystals, similar selection rules hold true for hexagonal crystals or tetragonal crystals when the direction of incident light is substantially parallel to the c-axis, and thus these crystals may also be used in the quantum circuit of the present invention. For example, II-VI group compounds such as zinc oxide (ZnO), zinc selenide (ZnSe), and cadmium sulfide (CdS) can also be considered. Even in the case of the existence of a quantum well or quantum box that confines electrons, the structure can be used if the structure maintains a prescribed symmetry. Organic compounds such as polyphilene may also be used. 
     A marked increase in the probability of two-photon absorption can be realized by inserting a two-photon absorbing crystal inside a structure in which light is confined within a narrow range to increase the electric field intensity. 
     One example of this type of structure is a Fabry-Perot resonator structure as shown in FIG.  7 : layer  63  including a two-photon absorbing crystal of one wavelength in thickness is sandwiched between multilayer mirrors  61  and  62  made up of alternately stacked two different types of semiconductor or dielectric. The incidence of light is substantially perpendicular to the reflecting mirrors. In order to separate the two transmitted light beams, the angle of incidence must be greater than 0°. 
     In this type of resonator, light is confined to approximately 10 μm 3 . In addition, the photon lifetime (the time that photons remain inside the resonator) is of the order of 10 ps. The intensity of the field that is produced inside the resonator by two photons in a Bell state is of the order of 104 V/m, wherein the refractive index of the layer that includes a two-photon absorbing crystal is assumed to be of the order of 3. 
     If cuprous chloride (CuCl) is used as the two-photon absorbing crystal, the two-photon absorption coefficient has a large value of 0.1 cm/W due to the giant two-photon absorption by exciton molecules. The speed of two-photon absorption inside the resonator reaches 0.1 ps −1 , whereby two-photon absorption occurs once during the photon lifetime and Bell states can be detected. 
     The structure of the resonator is not limited to a Fabry-Perot resonator. It is also possible to use a defect portion produced by disrupting periodicity in one portion of a photonic crystal: a photonic crystal is constituted by alternately arranging two or more substances having different dielectric constants at a period of the order of the wavelength of light. 
     A resonator realized by such a photonic crystal can confine light in a smaller volume than a Fabry-Perot resonator and also can extend the photon lifetime. Therefore, it allows a further increase in the probability of Bell-state detection. 
     It is also possible to raise the intensity of the electric field of light by means of a waveguide without using a resonator. Of course, a structure for confining light is not necessary if the two-photon absorption coefficient of a two-photon absorbing crystal is sufficiently large. 
     The present invention can finally be summarized as follows: 
     A specific Bell state is discriminated by using a two-photon absorbing crystal that absorbs a polarized photon pair of a specific Bell state in accordance with a selection rule based on the symmetry of the crystal; by using a polarization element, any Bell state of incident light can be converted to the specific Bell state to take part in the two-photon absorption by the concerned crystal; and thus alternate arrangement of a two-photon absorbing crystal and a polarization element makes it possible to discriminate any number of Bell states one by one. 
     A practical quantum circuit capable of discriminating a Bell state is thus provided without providing perturbation to atoms such as an external electromagnetic field in order to cause two-photon absorption of a specific Bell state, as is the case with a quantum circuit of the prior art. 
     The use of a crystal instead of a gas allows to intensify the two-photon absorption, thereby enabling detection of a Bell state with sufficiently high probability. In addition, by enabling the individual detection of the four Bell states, errors due to detection failures can be suppressed to a low level. 
     Finally, the present invention is not limited to the above-described embodiments, and each embodiment can obviously be modified as appropriate within the technological scope of the following claims.