Abstract:
Provided is an optical phase modulating method and apparatus for a quantum key distribution. When an optical phase modulator is arranged outside an optical interferometer, a configuration of the optical interferometer may be simplified, and an extension of an optical path caused by the optical phase modulator, instability and an insertion loss increased in the optical interferometer, and the like, may be overcome. An output feature may be improved by adjusting an applied voltage of the optical phase modulator arranged outside the optical interferometer.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of Korean Patent Application No. 10-2009-0128456, filed on Dec. 21, 2009, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference. 
     BACKGROUND 
     1. Field of the Invention 
     The present invention relates to a method that may arrange an optical phase modulator outside an interferometer and may modulate an optical phase in a phase modulation based quantum key distribution system. 
     2. Description of the Related Art 
     A quantum key distribution system may load key information on a single photon and may transmit the single photon to a receiver by adjusting a polarization or a phase of the single photon. A receiver may extract the key information using a polarization receiver, an optical phase modulator, and the like. The single photon transmission may be embodied based on optical communication technologies, and the quantum key distribution system intending to perform long-distance transmission may use a single mode optical fiber as a quantum channel. When a polarization-modulated single photon is transmitted through the single mode optical fiber, a polarization feature becomes unstable and thus, a phase modulation scheme is preferred for the key distribution than the polarization modulation scheme. 
     The phase modulation-based quantum key distribution system may mainly use a time-division optical interference scheme. An asymmetric optical interferometer and an optical phase modulator, and the like may be used to perform the time-division optical interference. The asymmetric optical interferometer may have two paths having different lengths, and the two paths may be used for an optical interference. A probability of existence of a single photon inputted to the asymmetric optical interferometer may be divided into two distributions of which probabilities of existence of the single photon have different coordinates in a time domain. The optical phase modulator modulates a phase of a single photon passing through one of the two paths. An asymmetric optical interferometer of the receiver may divide a probability of existence into four coordinates in the time domain. When a path difference of an asymmetric optical interferometer of a transmitter and a path difference of the asymmetric optical interferometer of the receiver are the same, adjacent two probabilities among the four probabilities of existence of the single photon may overlap with each other and may cause interference. The receiver may include an optical phase modulator, and the optical phase modulator may modulate a phase of the single photon. When a sum of phases modulated by the transmitter and the receiver is 2nπ, n being a natural number, the overlapped two probabilities of existence of the single photon may show a maximal detection probability by constructive interference, and when a sum of a sum of phases modulated by the transmitter and the receiver is (2n+1)π, the overlapped two probabilities of existence of single photon may shows a minimal detection probability by destructive interference. 
     A stability with respect to a polarization and a phase feature of the optical interferometer may be secured to obtain an excellent optical interfering performance. Two single photons interfering with each other may have the same polarization, and a phase with respect to an entire optical path, excluding a phase modulation value additionally provided by the optical phase modulator, may be maintained. 
     An optical interferometer for a conventional phase modulation based-quantum key distribution system may arrange the optical phase modulator inside an interferometer path. 
       FIG. 1  illustrates an example of a configuration of a conventional optical interferometer. A quantum key distribution system may include a transmitting-end  110 , a channel  120 , and a receiving-end  130 . The transmitting-end  110 , the channel  120 , and the receiving-end  130  may be connected with each other. The optical interferometer may be a Mach-Zehnder type interferometer. The optical interferometer may receive a photon from a light source  101 , and a delay line  103  and an optical phase modulator  104  used for constituting an asymmetric optical interferometer may be arranged between a beam splitter  102  and a beam splitter  105 . In the receiving-end  103 , a delay line  133  and an optical phase modulator  134  used for constituting the asymmetric optical interferometer may be arranged between a beam splitter  132  and a beam splitter  135 . Photon detection may be performed by two single photon detectors  138  and  139 . A high-speed optical phase modulator may be used for high-speed transmission of a quantum key. The high-speed optical phase modulator may be manufactured based on a LiNbO 3 -based planar lightwave circuit scheme. Both ends of a LiNbO 3 -based optical phase modulator may be pigtailed with optical fibers. When an optical modulator to which a pigtailed optical fiber is attached is inserted to the optical interferometer, a length of an optical path is extended and thus, instability of the optical interferometer may increase, and a configuration may become complex. The optical interferometer may be configured based on a polarization-dependent feature of the planar lightwave circuit and thus, difficulty in configuring the optical interferometer may increase. 
     The instability of the asymmetric optical interferometer due to the extended optical path may be caused by the following: 
     An optical fiber-based optical interferometer may be sensitive to a change in vibration and temperature. Specifically, an optical fiber may have a change in an effective length, as shown in Equation 1, due to a thermo-optic coefficient and a thermal expansion coefficient. As a length is extended and becomes longer, the change in the effective length may be higher. 
     
       
         
           
             
               
                 
                   
                     
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     In Equation 1, n may denote an effective refractive index, l may denote a length of the optical path, and T may denote a temperature. dn/dT may denote a thermo-optic coefficient and 1/l*dl/dT may denote a thermal expansion coefficient. An amount of change in an effective length of an optical path with respect to an asymmetric optical interferometer of transmitter and an amount of change in an effective length of an optical path with respect to an asymmetric optical interferometer of the receiver may be different, the transmitter and the receiver being in different environments. Therefore, relative phases of two single photons may not be maintained to be a predetermined value. 
     Unlike the example of  FIG. 1 , when a Michelson interferometer is used, the length of the optical path may be extended and become longer and thus, the instability may be higher. The optical phase modulator may basically include an insertion loss of several dBs and thus, a loss difference between two asymmetric paths may be relatively higher when the Michelson interferometer is applied. 
     Various schemes may be attempted to overcome difficulties of a conventional scheme. One attempt is decreasing of a length of a pigtailed optical fiber. However, there is limit to the decreasing of the length, since a predetermined length may need to be secured when an optical path may be constructed using an optical connector and an optical fiber fused connection, and the like. Another attempt is to not perform of pigtailing to the optical phase modulator. However, when the optical phase modulator to which the pigtail is not performed is applied to the optical fiber-based interferometer, a complex optical alignment problem may be incurred. 
     SUMMARY 
     An aspect of the present invention provides an apparatus and method of arranging an optical phase modulator and a phase modulation method thereof. 
     According to an aspect of the present invention, there is provided a transmitting apparatus of a quantum key distribution system, the transmitting apparatus including an optical interferometer to receive a single photon inputted from a light source, and to divide a path into a plurality of paths to enable a probability of existence of the inputted single photon to be distributed in a plurality of coordinates in a time domain, and an optical phase modulator being connected to an outside of the optical interferometer, and modulating a phase of a single photon corresponding to at least one path from among the plurality of paths. 
     The optical interferometer may include one of an optical fiber-based Mach-Zehnder interferometer and an optical fiber-based Michelson interferometer, and the optical interferometer may include one of an optical system-based Mach-Zehnder interferometer and an optical system-based Michelson interferometer. 
     According to an aspect of the present invention, there is provided a receiving apparatus of a quantum key distribution system, the receiving apparatus including an optical phase modulator to receive a single photon from a transmitting apparatus of a quantum key distribution system, and to modulate a phase of a single photon that is not modulated from the received single photon, and an optical interferometer to divide a path of the single photon received from the optical phase modulator to enable a probability of existence of the single photon received from the optical phase modulator to be distributed in a plurality of coordinates in a time domain, and the optical phase modulator is connected to an outside of the optical interferometer. 
     The optical interferometer may include one of an optical fiber-based Mach-Zehnder interferometer and an optical fiber-based Michelson interferometer, and the optical interferometer may include one of an optical system-based Mach-Zehnder interferometer and an optical system-based Michelson interferometer. 
     According to an aspect of the present invention, there is provided a quantum key distribution system, the system including a transmitting-end optical phase modulating unit including an optical phase modulator to input, with respect to a single photon, a modulation signal of which a time and a width is adjusted, a path of the single photon being divided into a plurality of paths to enable a probability of existence of the single photon to be distributed in a plurality of different coordinates, and to selectively modulate a phase of a single photon corresponding to at least one path from among the plurality of paths, and a receiving-end optical phase modulating unit to selectively modulate a phase of a single photon that is not modulated by the transmitting-end optical phase modulating unit from the single photon received via the transmitting-end optical phase modulating unit. 
     An applied voltage of the receiving-end optical phase modulating unit may be determined based on a phase difference between two optical interferometers respectively established in a transmitting-end and a receiving-end. In this case, the phase difference may be calculated based on a number of single photons detected with a maximal probability and a number of single photons detected with a minimal probability. 
     According to an aspect of the present invention, there is provided a transmitting method of a quantum key distribution system, the method including receiving a single photon inputted from a light source, performing an optical interfering process that divides a path of the single photon into a plurality of paths to enable a probability of an existence of the single photon to be distributed in a plurality of coordinates in a time domain, and performing an optical modulating process that modulates a phase of a single photon corresponding to at least one path from among the plurality of paths, outside an apparatus where the optical interfering process is performed. 
     According to an aspect of the present invention, there is provided a receiving method of a quantum key distribution system, the receiving method including performing an optical phase modulating process that receives a single photon transmitted via a transmitting-end, and modulates a phase of a single photon that is not modulated from the received single photon, and performing an optical interfering process that divides a probability of existence of the optical phase modulated-single photon to be distributed, with a plurality of different probabilities, in a time domain, and optical modulating process is performed separately from the optical interfering process. 
     According to an aspect of the present invention, there is provided an optical phase modulating method of a quantum key distribution system, the method including a transmitting-end optical phase modulating process of inputting, with respect to a single photon, a modulation signal of which a time and a width is adjusted, a path of the single photon being divided into a plurality of paths to enable a probability of existence of the single photon to be distributed in a plurality of different coordinates, and of selectively modulating a phase of a single photon corresponding to at least one path from among the plurality of paths, and a receiving-end optical phase modulating process of selectively modulating a phase of a single photon that is not modulated by the transmitting-end optical phase modulating process from the single photon received via the transmitting-end optical phase modulating process. 
     According to embodiments, when an optical phase modulator is arranged outside an optical interferometer, a configuration of an interferometer may be simplified, and it is easy to replace the optical interferometer with another interferometer having difference configuration. A path difference between two paths of an asymmetric optical interferometer may be easily set. Also, difficulties, such as extension of an optical path caused by the optical phase modulator, instability and an insertion loss increased in the optical interferometer, and the like, may be overcome. 
     According to embodiments, an output feature of an interferometer may be improved, for example, correction of a phase difference between an optical interferometer of a transmitter and an optical interferometer of a receiver may be accomplished by adjusting an applied voltage of the optical phase modulator arranged outside the optical interferometer. 
     Additional aspects, features, and/or advantages of the invention will be set forth in part in the description which follows and, in part, will be apparent from the description, or may be learned by practice of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and/or other aspects, features, and advantages of the invention will become apparent and more readily appreciated from the following description of embodiments, taken in conjunction with the accompanying drawings of which: 
         FIG. 1  is a diagram illustrating an example of a conventional optical interferometer; 
         FIG. 2  is a diagram illustrating a quantum key distribution system where an optical phase modulator is connected to an outside of an optical interferometer according to an embodiment of the present invention; 
         FIG. 3  illustrates detection probability distributions of a single photon when a time-division optical interference, namely, a constructive interference or a destructive interference, is performed according to an embodiment of the present invention; 
         FIG. 4  is a diagram illustrating examples where an optical phase modulator is arranged outside an optical fiber-based Mach-Zehnder interferometer and where an optical phase modulator is arranged outside an optical fiber-based Michelson interferometer, according to an embodiment of the present invention; 
         FIG. 5  is a diagram illustrating examples where an optical phase modulator is arranged outside an optical system-based Mach-Zehnder interferometer and where an optical phase modulator is arranged outside an optical system-based Michelson interferometer, according to an embodiment of the present invention; 
         FIG. 6  is a diagram illustrating a number of cases of a phase change based on a phase change incurred in each element unit of a quantum key distribution system and based on two outputs of an optical interferometer of a receiver according to an embodiment of the present invention; 
         FIG. 7  is a diagram illustrating an example of a phase modulation method and apparatus according to an embodiment of the present invention; 
         FIG. 8  is a diagram illustrating an example of constructing a transmitting-end optical phase modulating unit by successively arranging optical phase modulators; 
         FIG. 9  is a diagram illustrating a system that stabilizes an optical interferometer by correcting a phase difference incurred in the optical interferometer according to an example embodiment of the present invention; and 
         FIG. 10  is a flowchart illustrating a method of stabilizing an optical interferometer by correcting a phase difference incurred in the optical interferometer according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the like elements throughout. Embodiments are described below to explain the present invention by referring to the figures. 
       FIG. 2  illustrates a quantum key distribution system where an optical phase modulator is connected to an outside of an optical interferometer according to an embodiment of the present invention. 
     Referring to  FIG. 2 , a single photon from a light source  210  may be inputted to an optical interferometer  220 , and a path may be divided to enable a probability of existence to be distributed in two different coordinates in a time domain. An optical phase modulator  230  being connected to an outside of the optical interferometer  220  may phase-modulate a single photon corresponding to one of the two coordinates. After the single photon is transmitted via an optical fiber-based photon channel  240 , a single photon that is not phase-modulated may be phase-modulated in the optical phase modulator  250 . Two single photons may be divided and overlapped in an optical interferometer  260  and may be detected by a single photon detector  270 . 
       FIG. 3  illustrates detection probability distributions of a single photon when a time-division optical interference, namely, a constructive interference or a destructive interference, is performed according to an embodiment of the present invention. 
     Referring to  FIGS. 2 and 3 , the two single photons may be divided and overlapped in the optical interferometer  260  and may be detected by the single photon detector  270  with a single photon detection probability based on an optical interference, such as distributions of  FIG. 3 . Among four single photon distributions generated by two asymmetric optical interferometers, adjacent two single photon distributions may interfere with each other and the remaining two single photon distributions may not be interfered with. Single photons of probability distributions indicating probabilities that the single photon distributions are not interfered with, such as probability distributions  310 ,  330 ,  340  and  360 , may have predetermined detection value and thus, may not transmit any key. Adjacent two single photons may have a maximal detection probability  320  by constructive interference or may have a minimal detection probability  350  by destructive interference. 
     According to an embodiment of the present invention, the optical phase modulators  230  and  250  may be arranged outside the optical interferometers  220  and  260  and thus, the optical phase modulators  230  and  250  may be configured regardless of a type of optical interferometer. 
       FIG. 4  illustrates examples where an optical phase modulator is arranged outside an optical fiber-based Mach-Zehnder interferometer, and where an optical phase modulator is arranged outside an optical fiber-based Michelson interferometer, according to an embodiment of the present invention. 
     Referring to  FIG. 4 , in the example using the optical fiber-based Mach-Zehnder interferometer, a single photon inputted from a light source  410  may pass through a Mach-Zehnder interferometer  420  and may be phase-modulated by an optical phase modulator  430  being outside the optical fiber-based Mach-Zehnder interferometer  420 . Subsequently, the single photon may pass through a receiving-end optical phase modulator  450  via the quantum channel  440 , may pass through a Mach-Zehnder interferometer  460 , and may be detected by single photon detectors  471  and  472 . 
     Referring to  FIG. 4 , in the example using the Michelson interferometer, a single photon inputted from a light source  411  may pass through a Michelson interferometer  426  and may be phase-modulated by an optical modulator  431  being outside the Michelson interferometer  426 . Subsequently, the single photon may pass through a receiving-end optical phase modulator  451  via a quantum channel  441 , may pass through a Michelson interferometer  466 , and may be detected by single photon detectors  473  and  474 . 
     For example, although not illustrated, in the optical fiber-based Mach-Zehnder optical interferometers  420  and  460 , a polarization controller may be inserted into an optical path to enable polarizations of two output single photons of optical interferometer to be the same, or a polarization maintaining fiber may be used. The Michelson interferometers  426  and  466  may use a Faraday mirror to offset a change in a polarization on a path and thus, the polarizations of the two output single photons of the optical interferometer may be the same. 
       FIG. 5  illustrates examples where an optical phase modulator is arranged outside an optical system-based Mach-Zehnder interferometer, and where an optical phase modulator is arranged outside an optical system-based Michelson interferometer, according to an embodiment of the present invention. 
     Referring to  FIG. 5 , in the example using the optical system-based Mach-Zehnder optical interferometer, a single photon inputted from a light source  510  may pass through an optical system-based Mach-Zehnder optical interferometer  520  and may be phase-modulated by an optical phase modulator  530  being outside the Mach-Zehnder optical interferometer  520 . Subsequently, the single photon may pass through a receiving-end optical phase modulator  550  via a quantum channel  540 , may pass through an optical system-based Mach-Zehnder optical interferometer  560 , and may be detected by single photon detectors  571  and  572 . 
     Referring to  FIG. 5 , in the example using the optical system-based Michelson interferometer, a single photon inputted from a light source  511  may pass through an optical system-based Michelson optical interferometer  526  and may be phase-modulated by an optical phase modulator  531  being outside the Michelson optical interferometer  526 . Subsequently, the single photon may pass through a receiving-end optical phase modulator  551  via a quantum channel  541 , may pass through an optical system-based Michelson optical interferometer  566 , and may be detected by single photon detectors  573  and  574 . 
     When an optical phase modulator is arranged outside an optical interferometer, various advantages may be provided in addition to an example where a pigtailed LiNbO 3 -based optical phase modulator is applied. First, a configuration of an interferometer may be simplified, and it is easy to replace the optical interferometer with another interferometer having difference configuration. A path difference between two paths of an asymmetric optical interferometer may be easily set. Generally, a refractive index of the optical phase modulator is different from a refractive index of a Silica optical fiber constituting an optical path in the optical fiber-based optical interferometer, and is also different from a refractive index of air constituting an optical path in an optical system-based optical interference. The optical phase modulator may have an optical path based on a thickness or a length of the optical phase modulator. Therefore, when the optical phase modulator is eliminated from the optical path, the length of the optical path of an interferometer may be simply calculated. 
     According to an embodiment, when the optical phase modulator is arranged outside the optical interferometer, a transmitting-end optical phase modulator and a receiving-end optical phase modulator may perform a phase modulating process based on a method different from a conventional method. The conventional method may arrange the optical phase modulator in one side of the asymmetric optical interferometer and thus, a single photon of which a path is divided into two paths may be modulated regardless of the single photon&#39;s relative location. However, according to an embodiment, two adjacent single photons may be phase-modulated while being transmitted and thus, the phase-modulation may be selectively performed and the phase-modulation may be performed based on interference incurred after the two single photons pass through the receiving optical interferometer. 
       FIG. 6  illustrates a number of cases of a phase change based on a phase change incurred in each element unit of a quantum key distribution system and based on two outputs of an optical interferometer of a receiver according to an embodiment of the present invention. 
     Referring to  FIG. 6 , a single photon inputted from a light source  610  may pass through an optical interferometer  620  of transmitting-end and may sequentially pass through a transmitting-end optical phase modulator  630 , a quantum channel  640 , a receiving-end optical phase modulator  650 , and an optical interferometer  660  of a receiving-end. 
     Referring to  FIG. 6 , the single photon passing through two asymmetric optical interferometers may show three single photon detection distributions. In this case, two fixed detection distributions that may not contribute interference may be generated when the single photon passes through a shot path, namely, a path excluding an optical delay  622  and an optical delay  662 , or when the single photon passes through a long path, namely, a path including the optical delay  622  and the optical delay  662 . When a single photo passing through the short path in a first optical interferometer  620  among two asymmetric optical interferometers and passing through the long path in a second optical interferometer  660  meets a single photon passing through in the opposite way, interference may be incurred. Unlike an optical interferometer  620  of a transmitter, the optical interferometer  660  of the receiver may use two outputs of a beam splitter  663 , namely, output  1  and output  2 . In this case, two outputs have a phase difference of π. When one side shows a constructive interference output, the other side shows a destructive interference output. A contrast between two outputs may clarify a detection result. Referring to  FIG. 6 , beam splitters  621 ,  623 ,  661 , and  663  may generally be embodied based on a 2×2 optical coupler. In the 2×2 optical coupler, a phase change may not be incurred for a parallel input and output, whereas a phase change of π/2 may be incurred for an output crossing over an input. In a beam splitter used for an optical system-based optical interferometer, when an input is projected from a side of air to a boundary surface between the air and the medium, a phase change of π may be accompanied by only a reflection of a transverse magnetic mode wave, and a phase change may not be incurred by remaining cases. Conversely, when the input is projected from a side of the medium, a phase change of π may be accompanied by only a reflection of a transverse electric mode wave, and a phase change may not be incurred by remaining cases. With respect to a case where the optical phase modulator is arranged outside the optical system-based optical interferometer, a phase change of each element unit, such as beam splitters and optical delays  622  and  662  in the optical interferometer, and optical phase modulators  630  and  650 , may be organized for each type of path, namely, a short path and a long path, and may be illustrated beneath a corresponding element unit. Although the optical system-based optical interference interferometer is used, an operation principle may be the same. 
     Table 1 may organize a phase of a final interference light that may be generated by a combination of paths of the two asymmetric optical interferometer of  FIG. 6  according to an embodiment of the present invention. 
     
       
         
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Phase of path 1 
                 Phase of path 2 
                   
               
               
                   
                 (short path + 
                 (long path + 
                 Phase 
               
               
                 Output 
                 long path) 
                 short path) 
                 difference 
               
               
                   
               
             
             
               
                 Output 
                 (0 + 0 + π/2 + Φ A ) + 
                 (π/2 + 0 + 0 + 0) + 
                 Φ A  − Φ B   
               
               
                 1 
                 (0 + 0 + 0 + π/2) 
                 (Φ B  + π/2 + 0 + 0) 
               
               
                 Output 
                 (0 + 0 + π/2 + Φ A ) + 
                 (π/2 + 0 + 0 + 0) + 
                 Φ A  − Φ B  − π 
               
               
                 2 
                 (0 + 0 + 0 + 0) 
                 (Φ B  + π/2 + 0 + π/2) 
               
               
                   
               
             
          
         
       
     
     Referring to Table 1, two outputs  671  and  672  of a receiving-end may have a phase difference of π, and the receiving-end may have various outputs based on an amount of phase modulation performed by the transmitting-end optical phase modulator  630  and the receiving-end optical phase modulator  650 . When the transmitting-end optical phase modulator  630  and the receiving-end optical phase modulator  650  allow the same phase modulation, an output  1   671  may show a maximal single photon detection probability by constructive interference and an output  2   672  may show a minimal probability by destructive interference. 
       FIG. 7  illustrates an example of a phase modulation method and apparatus according to an embodiment of the present. 
     Referring to  FIG. 7 , a height of a vertical arrow denotes a detection probability of a single photon. A number marked above the arrow denotes a relative phase of the single photon. A single photon may be outputted from a light source  710 , may pass through an optical interferometer  720 , and may be inputted to a transmitting-end optical phase modulator  730 . The transmitting-end optical phase modulator  730  may modulate a phase of at least one of two single photons by Φ A    731 . After the two single photons pass through a channel  740 , a receiving-end optical phase modulator  750  may modulate a phase of a single photon that is not phase-modulated by the transmitting-end optical phase modulator  730  by Φ B    751 . A modulation signal of which a time and a width are adjusted may be inputted to the optical phase modulators  730  and  750 , to selectively modulate the two single photons. A graph of a modulation signal to be inputted to the transmitting-end optical phase modulator  730  and a graph of a modulation signal to be inputted to the receiving-end optical phase modulator  750  are illustrated respectively beneath relative locations  731  and  751  on a time axis where a phase of a corresponding single photon is to be modulated. 
     Although the present embodiment describes that the transmitting-end optical phase modulator  730  may modulate a phase of a preceding single photon by Φ A , the transmitting-end optical phase modulator  730  may modulate a phase of a following single photon. In this example, the receiving-end optical phase modulator  750  may modulate a phase of a single photon that is not phase-modulated by the transmitting optical phase modulator  730 . 
     From an output  1   771  of an optical interferometer  760  of a receiver, two single photon detection distributions of two single photons that are unrelated to interference and are respectively phase-modulated by Φ A  and Φ B  may be outputted with a probability of 1/16, and a single photon detection distribution of a single photon interfering based on a phase difference of Φ A −Φ B  may be outputted with a probability of ⅛. A single photon distribution of a single photon interfering based on a phase difference of Φ A −Φ B −π it may be outputted to a center of an output  2   772 . 
     Table 2 illustrates an example of a phase modulation based quantum key distribution method. Table 2 organizes an amount of phase modulation allowed by an optical phase modulator of each of a transmitter and the receiver, after a quantum key distribution protocol being referred to as Bennett Brassard 84 (BB84) is applied. 
     
       
         
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Stage 
                 Contents 
                 value 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 Transmitting-end bit info. 
                 0 
                 1 
                 0 
                 1 
               
             
          
           
               
                   
                 Transmitting-end basis 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
               
               
                   
                 info. 
               
               
                 2 
                 Transmitting-end 
                 0 
                 π/2 
                 π 
                 3π/2 
                 0 
                 π/2 
                 π 
                 3π/2 
               
               
                   
                 phase modulation (Φ A ) 
               
             
          
           
               
                 3 
                 Receiving-end basis info. 
                 0 
                 1 
               
               
                 4 
                 Receiving-end phase 
                 0 
                 π/2 
               
               
                   
                 modulation (Φ B ) 
               
             
          
           
               
                 5 
                 Output 1 interference 
                 0 
                 π/2 
                 π 
                 3π/2 
                 −π/2 
                 0 
                 π/2 
                 π 
               
               
                   
                 light phase difference 
               
               
                   
                 (Φ A  − Φ B ) 
               
               
                   
                 Output 2 interference 
                 −π 
                 −π/2 
                 0 
                 π/2 
                 −3π/2 
                 −π 
                 −π/2 
                 0 
               
               
                   
                 light phase difference 
               
               
                   
                 (Φ A  − Φ B  − π) 
               
               
                 6 
                 Detection probability of 
                 Max 
                 ? 
                 Min 
                 ? 
                 ? 
                 Max 
                 ? 
                 Min 
               
               
                   
                 detector 1 
               
               
                   
                 Detection probability of 
                 Min 
                 ? 
                 Max 
                 ? 
                 ? 
                 Min 
                 ? 
                 Max 
               
               
                   
                 detector 2 
               
               
                   
               
             
          
         
       
     
     Referring to  FIG. 2 , the transmitting-end optical phase modulator  230  may perform four levels of phase modulations by combining bit information corresponding to a quantum key and basis information enabling a secure communication. Each bit may have two orthogonal basis information. The basis information may be randomly generated. Therefore, a single photon having a phase value, such as 0, π/2, π, 3π/2, and the like, may be generated. A receiving-end may randomly generate two orthogonal basis information and may apply the generated information without being combined with bit information. In this case, the receiving-end optical phase modulator  250  may phase-modulate the single photon by 0 or π/2, or may phase-modulate the single photon by π or 3π/2. Generally, for convenience of operation of the receiving-end optical phase modulator  250 , the single photon may be modulated by 0 or π/2 to provide the orthogonal basis information. 
     In this case, an optical interference due to the phase modulation of Table 2 may be incurred. In Table 2, a question mark, namely, “?”, denotes a case where a single photon is detected, by the single photon detector  270 , with a probability that is different from a maximal probability and a minimal probability, since basis information randomly generated from a transmitting-end is different from the basis information randomly generated from the receiving-end. The result may be deleted because the result is regarded as invalid data during a basis information exchanging process of the quantum key distribution system and thus, the result may not have any value of regard in operation of an optical interferometer. 
       FIG. 8  illustrates an example of constructing a transmitting-end optical phase modulating unit  830  by successively arranging optical phase modulators. 
     Referring to  FIG. 8 , a four-level phase modulation of a transmitting-end may be performed based on a scheme of successively using two optical phase modulators. Specifically, the optical phase modulators may be successively arranged so that one  831  of the two optical phase modulators modulates a phase of a single photon based on bit information and a remaining optical phase modulator  832  may modulate a phase of the single photon based on basis information. The optical phase modulator modulating the phase of the single photon corresponding to the bit information and the optical phase modulator modulating the phase of the single photon corresponding to the basis information may be arranged in a different sequence. 
     An output feature of an optical interferometer may be improved based on the optical phase modulating method according to an embodiment of the present invention. According to an embodiment of the present invention, an optical phase modulator is arranged outside an optical interferometer to easily configure the optical interferometer and thus, instability of the optical interferometer may be prevented. In addition, the optical phase modulator arranged outside the optical interferometer may stabilize the optical interferometer. 
       FIG. 9  illustrates a system that stabilizes an optical interferometer by correcting a phase difference incurred in the optical interferometer according to an example embodiment of the present invention. 
     Referring to  FIG. 9 , a path difference of an asymmetric optical interferometer of a transmitter and a path difference of an asymmetric optical interferometer of the receiver may be changed depending on an environment, such as different external temperatures, vibration, and the like. In this case, two outputs of an optical interferometer may indicate a value that may be different from a maximal detection probability and a minimal detection probability. According to an optical interferometer method, a processing and control unit  980  may continuously monitor a number of single photons detected by single photon detectors  971  and  972 . An optical interferometer visibility (V) may be calculated based on the number of detected single photons as given in Equation 2. 
     
       
         
           
             
               
                 
                   V 
                   = 
                   
                     
                       
                         
                           C 
                           max 
                         
                         - 
                         
                           C 
                           min 
                         
                       
                       
                         
                           C 
                           max 
                         
                         + 
                         
                           C 
                           min 
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 2, C max  may denote a number of photons detected with a maximal probability, and C min  may denote a number of photons detected with a minimal probability. A change in V may be incurred due to a phase difference (ΔΦ) between an optical interferometer of a transmitting-end and an optical interferometer  960  of a receiving-end, and may satisfy Equation 3. 
     
       
         
           
             
               
                 
                   
                     
                       1 
                       - 
                       V 
                     
                     2 
                   
                   = 
                   
                     
                       
                         sin 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           ΔΦ 
                           2 
                         
                         ) 
                       
                     
                     . 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ] 
                 
               
             
           
         
       
     
     A change in the phase difference may be calculated based on a change in the number of detected single photons, using Equation 2 and Equation 3. An applied voltage may be adjusted by an applied voltage controller  990  based on the change in the phase difference when a receiving-end optical phase modulator  950  is operated. A voltage used by the receiving-end optical phase modulator to cause a change of a phase difference of π may be Vπ. Therefore, when the receiving-end optical phase modulator operates, Vα may be additionally provided to provide an additional change of α (=π/Vπ×Vα=ΔΦ) for the phase. In this manner, a phase difference between the optical interferometer of a transmitter and the optical interferometer  960  of a receiver may be corrected using the optical phase modulator arranged outside the interferometer. 
     Referring to  FIG. 9 , a graph at the top of  FIG. 9  may be an example of a phase modulation signal of the receiving-end optical modulator to which Vα is additionally applied. 
       FIG. 10  illustrates a method of stabilizing an optical interferometer by correcting a phase difference incurred in the optical interferometer according to an embodiment of the present invention. 
     A single photon is received from a light source in operation S 1010 . 
     A path is divided into a plurality of paths to enable a probability of existence of the single photon to be distributed in a plurality of different coordinates in a time domain in operation S 1020 . In this case, an interfering method may be a Mach-Zehnder optical interfering method or a Michelson optical interfering method, and may be performed based on an optical fiber or an optical system. Also, a polarization maintaining fiber or a polarization controller may be used. 
     A modulation signal of which a time and a width are adjusted is inputted to selectively modulate a phase of a single photon corresponding to at least one of the plurality of paths in operation S 1030 . Therefore, the modulation signal of which the time and the width are adjusted may be inputted. 
     Optical phase modulations may be successively performed. In this case, one of the optical phase modulations may modulate a phase of a single photon based on bit information, and a remaining optical phase modulation may modulate a phase of the single photon based on basis information. 
     The single photon passes through a quantum channel in operation S 1040 . The quantum channel may be based on an optical fiber. 
     A phase of a single photon that is not modulated in operation S 1030 , from the single photon received via the quantum channel, may be selectively modulated in operation S 1050 . In this case, the modulation signal of which a time and a width are adjusted may be inputted. 
     Subsequently, a path of the single photon is divided into a plurality of paths to enable a probability of existence of the single photon to be distributed in a plurality of different coordinates in a time domain in operation S 1060 , which is an optical interfering process. In this case, the interfering method may be a Mach-Zehnder optical interfering method or a Michelson interfering method, and may be performed based on the optical-fiber or the optical system. Also, the polarization maintaining fiber or the polarization controller may be used. 
     A single photon detector detects an outputted single photon in operation S 1070 . 
     In this case, an optical interferometer visibility is calculated based on a number of detected single photons, and a phase difference (ΔΦ) between two optical interfering processes of operations S 1020  and S 1060  is calculated in operation S 1080 . Equation 2 and Equation 3 may be used for the calculation. C max  may denote a number of single photons detected with a maximal probability and C min  may denote a number of single photons detected with a minimal probability. When ΔΦ is not incurred, the detecting process may be terminated. 
     When ΔΦ is incurred, an applied voltage of an optical phase modulating process may be adjusted based on ΔΦ. During the optical phase modulating process, a voltage used to cause a phase change of π may be Vπ. Therefore, when an optical phase modulating process is performed in operation S 1050 , Vα may be additionally provided to provide an additional change of α (=π/Vπ×Vα=ΔΦ) for the phase in operation S 1090 . 
     In this manner, the phase difference between the optical interference processes may be corrected by optical modulating processes of operations S 1030  and S 1050  that are separately operated from interfering processes of operations S 1020  and S 1060   
     The phase difference may be corrected without operations S 1080  and S 1090 . 
     The optical phase modulation method has been described. Descriptions described with reference to  FIGS. 2 through 9  may be applicable to the optical phase modulation method and thus, detailed descriptions thereof will be omitted. 
     Although a few embodiments of the present invention have been shown and described, the present invention is not limited to the described embodiments. Instead, it would be appreciated by those skilled in the art that changes may be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.