JP5526087B2 - Quantum entanglement generation system, entanglement generation method - Google Patents

Description

  The present invention relates to a entanglement generation system and a entanglement generation method that generate entanglement based on transmission of a pulse in a coherent state.

  In order to perform quantum communication, it is necessary that at least the transmission / reception apparatus has the ability to share quantum entanglement. The sharing of the quantum entanglement is achieved by transmitting one of the two systems in the quantum entangled state to the receiving apparatus and performing a generalized measurement on the system received by the receiving apparatus. This implies that the quantum entanglement generation method is defined by “quantum entangled state prepared by the transmitter” and “generalized measurement performed by the receiver”. Some conventional quantum entanglement generation methods are based on the fact that a transmission device generates a “quantum entangled state between coherent states of a qubit and an optical”. Quantum communication based on coherent state transmission is generally considered to be included in the following framework for entanglement generation. With reference to FIG. 1, the concept of entanglement generation based on coherent state transmission will be described. FIG. 1 is a diagram illustrating a concept of entanglement generation based on transmission in a coherent state.

<Procedure 1>
First, the transmitting device uses some method to store its own qubit A (see Appendix A) [2] and optical pulse μ [1].

The quantum entangled state [6] is prepared. Here, {q _j } _{j = 0,1} is a probability distribution, {| j>} _{j = 0,1} is a calculation basis of qubit A, and {| α _j >} _{j = 0,1} is an optical pulse. Is in a coherent state. Note that the quantum mechanical description of the pulse produced by the laser corresponds to the coherent state. Since the coherent state is characterized by a complex number α, it is described as | α>. | Α | corresponds to the amplitude of the laser beam.

<Procedure 2>
Next, the transmission device transmits the optical pulse μ to the reception device through a transmission path (optical fiber, in vacuum, in air, etc.) [9]. The pulse received by the receiving device will be referred to as ν ₁ [4]. Since there is generally optical loss in the transmission line, the action of the transmission line includes the state of the environmental system E [3],

[7]. here,

Also represents a coherent state. T corresponds to the transmittance of the transmission line. If T is large, it means that the optical loss in the transmission line is small. Therefore, from the equation (2), when the receiving device receives the optical pulse ν ₁ , the state [8] of the entire system including the environment system is

Will be written.

<Procedure 3>
Next, the receiving apparatus performs generalized measurement [5] on the received optical pulse ν ₁ [4], and determines the success / failure of the entanglement sharing according to the measurement result.

  Quantum entanglement generation based on transmission in a coherent state also plays a fundamental role in quantum relay, which is a technique for extending the distance of quantum communication (see Non-Patent Documents 2 to 6). The purpose of entanglement here is to provide entanglement between distant matter qubits, which can be used between optical pulses and various matter qubits (details are not patented) Unitary interaction (see reference 2)

It is. An example of how to implement this unitary operation is shown in Appendix B. Here, {| αe ^{± iθ / 2} >} is a coherent state. In fact, this interaction ^ U

The material qubit A in the state and the optical pulse μ in the coherent state | α> _μ are given by the rule of the equation (4):

A system for generating entanglement through <Procedure 2> to <Procedure 3> has been proposed. These existing quantum entanglement generation systems are different in procedure 3 in that (a) a system that uses only one detection light (Non-Patent Documents 2, 3, and 4) and (b) a system that uses two detection lights ( Non-Patent Documents 5 and 6). Here, the detection light refers to an optical pulse that interacts with a qubit. In a system using only one detection light, the receiving device makes the received light pulse ν ₁ incident on the material qubit B held by itself, so the light pulse input to the material qubit AB. There is only one (Non Patent Literature 2, 3, 4). On the other hand, in a system that uses two detection lights, the receiving device enters the light pulse ν ₂ initialized to a coherent state, separately from the received light pulse ν ₁ , into the material qubit B held by itself. The detection light for the bit A is ν ₁ , the detection light for the material qubit B is ν ₂ , and two light pulses are used (Non Patent Literatures 5 and 6).

  Hereinafter, a conventional entanglement generation system 9 (Non-Patent Documents 5 and 6) using two detection lights will be described with reference to FIGS. FIG. 2 is a block diagram showing a configuration of a prior art quantum entanglement generation system 9 using two detection lights. FIG. 3 is a flowchart showing the operation of the conventional entanglement generation system 9 using two detection lights. The prior art quantum entanglement generation system 9 includes a transmission device 80, a reception device 90, and a transmission line 100. The transmission device 80 includes a qubit A81, a first interaction unit 82, and a first switch 84. The first interaction unit 82 includes a beam splitter 82a. The receiving device 90 includes a second switch 91, a qubit B92, a second interaction unit 93, a detection light generation unit 94, a first displacement calculation unit 95, a detection unit 96, and a determination unit 97. . The second interaction unit 93 includes a beam splitter 93a. The detection light generation unit 94 includes a beam splitter 94a. The first displacement calculation unit 95 includes a beam damper 95a and a beam splitter 95b. The detection unit 96 includes a photon detector 96a and a photon detector 96b. The entanglement generation system 9 is defined as follows with respect to the transmittance T (0 ≦ T ≦ 1) of the transmission line 100 (Non-Patent Documents 5 and 6).

<Procedure 1>
The quantum bit A81 of the transmitter 80 is set as ζ _α = (α ² sin θ) / 2,

(S81). Next, the beam splitter 82a of the first interaction unit 82 irradiates the qubit A81 with the light pulse μ in the coherent state | α / √T> _μ (where α ≧ 0), and the equation (4) Quantum entangled state through unitary transformation ^ U

Is prepared (S82). However, ζ _α is not an essential parameter, and is only introduced so as to facilitate the mathematical handling of the state of the system.

<Procedure 2>
The first switch 84 transmits the optical pulse μ together with the reference light LO to the receiving device 90 through the transmission line 100 (S84). The pulse received by the receiving device 90 is called ν ₁ . From equation (2), the state of the entire system is

It becomes.

<Procedure 3>
The second switch 91 of the receiving device 90 receives the optical pulse ν ₁ and the reference light LO from the transmitting device 80 (S91). The qubit B92 is ^{initialized to} (e− ^iζα | 0> _B + ^eiζα | 1> _B ) / √2 (S92). The beam splitter 93a of the second interaction unit 93 is in a coherent state from the received reference light LO.

₂ is prepared and is incident on the qubit B92 initialized to (e− ^iζα | 0> _B + ^eiζα | 1> _B ) / √2 (S93). By this operation, similarly to the derivation of Equation (5), the optical pulse ν ₂ and the qubit B92 of the receiving device 90 are

It becomes.

<Procedure 4>
The detection light generation unit 94

The beam splitter 94a is a 50/50 beam splitter defined by Accordingly, the detection light generation unit 94 receives the pulsed light ν ₁ and the pulsed light ν ₂ and causes the 50/50 beam splitter 94a to act to generate the pulsed light ν ₃ and the pulsed light ν ₄ (S94). .

<Procedure 5>
The first displacement calculation unit 95 performs a displacement operator on the pulse ν ₄ .

(S95). In general, the displacement operator ^ D _β changes the coherent state | α> to the coherent state | α + β>

And convert. Therefore, the state of the entire system at this point is

This is the state immediately before the measurement.

<Procedure 6>
The detection unit 96 includes a photon detector 96a and a photon detector 96b. Photon detector 96a and the photon detector 96b measures the pulse light [nu ₃ and pulsed light [nu ₅ respectively (S96). When one of the photon detectors detects a photon, the determination unit 97 determines that the quantum entanglement has been successfully shared (S97).

W. K. Wootters, "Entanglement of Formation of an Arbitrary State of Two Qubits", Phys. Rev. Lett. 80, pp2245-2248 (1998). P. van Loock, TD Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, WJ Munro, and Y. Yamamoto, "Hybrid Quantum Repeater Using Bright Coherent Light", Phys. Rev. Lett. 96, 240501 (2006) . P. van Loock, N. Lutkenhaus, W. J. Munro, and K. Nemoto, "Quantum Repeaters using Coherent-State Communication", Phys. Rev. A 78, 062319 (2008). W. J. Munro, R. Van Meter, S. G.R.Louis, and K. Nemoto, "High-Bandwidth Hybrid Quantum Repeater", Phys. Rev. Lett. 101, 040502 (2008). K. Azuma, N. Sota, R. Namiki, SK Ozdemir, T. Yamamoto, M. Koashi, and N. Imoto, "Optimal entanglement generation for efficient hybrid quantum repeaters", Phys. Rev. A 80, 060303 (R) (2009). K. Azuma, H. Takeda, M. Koashi, and N. Imoto, "Quantum repeaters and computation by a single module", e-print arXiv: 1003.0181. K. Azuma, N. Sota, M. Koashi, and N. Imoto, "Tight bound on coherent-state-based entanglement generation over lossy channels", Phys. Rev. A 81, 022325 (2010).

  In general, there are two types of errors that occur in quantum entanglement: “bit error” and “phase error”, but the quantum entanglement generation system 9 in FIG. 2 has one type of error that the generated quantum entanglement has. Designed to. Such a design that “limits the type of error included in the generated quantum entanglement to one” is not limited to the quantum entanglement generation system 9 but an existing system that uses only one detection light (Non-Patent Documents 3 and 4). ). This means that so far, emphasis has been placed on entanglement generation systems in which errors generate one type of entanglement. Also, for any system that currently generates one type of entanglement, the error type is defined as “success probability” and “average value of fidelity of entanglement generated under successful conditions”. The existence of theoretical limits has been clarified (Non-Patent Document 7). It has also been proved that this theoretical limit can be achieved by the entanglement generation system 9 of FIG. 2 using an ideal photon number identification detector (Non-patent Document 7).

  As described above, the conventional system is designed to satisfy the restriction that “the kind of generated entanglement error is one”, and as a result, the entanglement generation system 9 of FIG. 2 is optimal within this restriction. It has been made clear. However, if the number of types of entanglement errors generated is not adhered to, there is a possibility that a more efficient system than an existing system can be constructed.

  Therefore, an object of the present invention is to provide a quantum entanglement generation system that can achieve efficiency close to the theoretical limit in the case where the type of error is not limited by not limiting the type of error.

  The quantum entanglement generation system of the present invention includes a transmission device, a transmission line having a transmittance T that can cancel a phase change received by an optical pulse during transmission, and a reception device. The transmission device includes a qubit A and a first entanglement generation unit. The receiving device includes a qubit B, a second entanglement generation unit, a detection light generation unit, a detection unit, and a determination unit.

The first entanglement generator, ₀ complex α representing the coherent light amplitude and phase qubit A corresponds to the state of _0, a complex number representing the coherent light amplitude and phase qubit A corresponds to one state as the alpha _1, entangled state of the quantum bit a and the optical pulse μ

And the optical pulse μ is transmitted through the transmission path (transmittance T). The light pulse that has passed through the transmission path shall be referred to as the optical pulse [nu _1, including when the E denote the state of the light pulse that has leaked to the environment system, environmental system after the transmission path passing through the optical pulses [nu ₁ total The state of the system is

It becomes.

Generator entangled second quantum is ₀ complex β representing the coherent light amplitude and phase qubit B corresponds to the state of _0, a complex number representing the coherent light amplitude and phase of the qubit B corresponds to the first state Is the entangled state of qubit B and optical pulse ν ₂ with β ₁

Is generated. The detection light generation unit receives the light pulse ν ₁ and the light pulse ν ₂ and inputs the state of the entire system.

(Where a: = | α ₀ −α ₁ | / 2, b: = | β ₀ −β ₁ | / 2 is an arbitrary real number satisfying a ≠ b, and θ ₀ , θ ₁ , θ _p , θ _q Are generated as optical pulses ν ₃ and ν ₄ . Detector, the value depending on the number of photons of the optical pulse [nu _3, and a value dependent on the photon number of light pulses [nu ₄ measures. Determination unit determines whether there is a difference in the number of photons of light pulses [nu ₃ and the optical pulse [nu ₄ had estimated, the value depending on the number of photons measured light pulses [nu ₃ and the light pulses [nu ₄ photons If it is estimated from the value depending on the number that there is a difference in the number of photons held by the optical pulse ν ₃ and the optical pulse ν _4, it is determined that the sharing of the quantum entanglement is successful, and the measured optical pulse ν ₃ and the value dependent on the number of photons of the optical pulse ν ₄ , it is estimated that “there is no difference in the number of photons of the optical pulse ν ₃ and the optical pulse ν ₄ ”. Determine that tangle sharing has failed.

<Theoretical limits in the entanglement generation system of the present invention>
As a result of deriving a general theoretical limit for the “quantum entanglement generation method without limiting the type of error” as in the present invention, the “success probability P _{s of the} method” and the “concurrence of generated entanglement ( For the average value ￣C ”of one of the indices representing the intensity of entanglement (see Non-Patent Document 1),

The theoretical limit (graph of FIG. 12 (i)) has been found. On the other hand, the success probability P _s of the entanglement generation system 9 of FIG.

(Graph of FIG. 12 (iii)), it can be seen that there is a gap from the theoretical limit of equation (13). Furthermore, even when compared with the efficiency of another existing method (FIGS. 12 (iv) and (v)), there is a gap between the theoretical limit of equation (13) (graph of FIG. 12 (i)). If the gap between the theoretical limit (13) and the efficiency of the existing scheme does not stick to the number of types of generated entanglement errors, a more efficient entanglement generation scheme can be constructed. It suggests that there is.

  The quantum entanglement generation system of the present invention has actually realized a more efficient quantum entanglement generation method than the existing method by allowing generation of quantum entanglement including a plurality of errors. This scheme can achieve the theoretical limit (13) if some kind of quantum nondestructive measurement is available, and even if the role of quantum nondestructive measurement is replaced by a photon detector, the theoretical limit (13) Boasting an efficiency close to (the graph of FIG. 12 (ii)).

<Verification of the effect of the entanglement generation system of the present invention>
If the parameters α ₀ , α _1, β _{0 and} β ₁ are selected so that the parameters a and b in the equation (22 ′ ″) are equal, the type of error that the generated quantum entanglement has is 1 It is limited to seeds, and it behaves similarly to the entanglement generation system 9 of FIG. Unlike the quantum entanglement generation system 9 of FIG. 2, the present invention does not limit the types of errors that are generated, i.e., does not impose the condition that a and b are equal, thereby achieving an efficiency comparable to the theoretical limit (13). It is a system that achieves.

  Here, in order to see the effect of the invention,

Discuss as. As an example, the receiving device as a detection unit,

Quantum nondestructive measurement corresponding to the projection operator is used. In this case, the system generates quantum entanglement between the qubit A and the system Bν ₃ ν ₄ of the receiving device, and the efficiency of this scheme coincides with the theoretical limit (13) (FIG. 12 (i)).

Assuming that the receiving device is a detection unit and measures the number of photons of each of the light pulse ν ₃ and the light pulse ν ₄ with an ideal photon number identification detector, the success probability P of the quantum entanglement generation system of the present invention _s is

It is represented by Where I _α is the modified Bessel function

Represents. In addition, the average value ￣C of the entanglement concurrence generated upon success is

Can be written. Therefore, it can be seen that the success probability P _s and the concurrence ￣C are controlled by a and b. If b = a, the quantum entanglement generated by this scheme has not only one type of error, but the efficiency of this scheme is equal to the efficiency of the existing scheme described above [Equation (14)]. However, unlike the above-described system (Non-Patent Document 5), this method still has the degree of freedom of the parameter b, and thereby the efficiency of this method exceeds that of the above-described system (Non-Patent Document 5). For example, as a way of selecting a and b, for a desired success probability P, a and b are such that the concurrence ￣C is maximized.

It is also possible to determine from

  As an example, the efficiency of formula (25), the efficiency of the existing scheme, and the theoretical limit [formula (13)] are illustrated in FIG. FIG. 12 is a diagram showing a comparison between the concurrence and success probability of the prior art and the concurrence and success probability in the present invention. In FIG. 12, for comparison, the transmission line corresponds to an optical fiber of 0.17 dB / km, and its transmittance T is

And θ is assumed to be 0.01, and all detectors utilized in each scheme are assumed to be ideal. The horizontal axis is the success probability of the method, and the vertical axis is the average value of the entanglement of entanglement generated upon success. (I) is the theoretical limit when the type of error is not limited [Expression (13)], (ii) is the efficiency of the quantum entanglement generating system of the present invention [Expression (25)], and (iii) is the two detection lights. Efficiency [Formula (14)] and (iv) of the existing system (Non-Patent Documents 5 and 6) to be used is the efficiency of the existing system (Non-Patent Document 2) based on the homodyne detector and one detection light, (v) Represents the efficiency of existing systems (Non-Patent Documents 3 and 4) based on a photon detector and one detection light, respectively. From the graph it can be seen that the efficiency of the quantum entanglement system of the present invention is not only very close to the theoretical limit, but also exceeds the efficiency of all existing systems. Therefore, the quantum entanglement generation system of the present invention shows that the efficiency of quantum entanglement generation is improved by removing the “constraint on error of generated quantum entanglement” that the existing system has adhered to. In this calculation, it is assumed that the photon detector used in the detector is an ideal photon number identification detector. However, even if a general photon detector is used, the quantum entanglement generation system of the present invention functions, The efficiency of the quantum entanglement generating system of the present invention is controlled by the parameters a and b in the equation (22 ′ ″).

  As described above, according to the present quantum entanglement generation system, the efficiency close to the theoretical limit [Equation (13)] when the error type is not limited can be achieved by not limiting the error type. In the following, an example for constructing the formula (22 ′ ″) will be shown.

The figure which shows the concept of the entanglement production | generation based on transmission of a coherent state. The block diagram which shows the structure of the quantum entanglement generation system of a prior art. The flowchart which shows operation | movement of the quantum entanglement generation system of a prior art. 1 is a block diagram illustrating a configuration of a entanglement generation system according to Embodiment 1. FIG. 3 is a flowchart illustrating the operation of the quantum entanglement generation system according to the first embodiment. FIG. 3 is a block diagram illustrating a configuration of a quantum entanglement generation system according to a second embodiment. 9 is a flowchart showing the operation of the quantum entanglement generation system according to the second embodiment. FIG. 9 is a block diagram illustrating a configuration of a quantum entanglement generation system according to a third embodiment. 10 is a flowchart illustrating an operation of the quantum entanglement generation system according to the third embodiment. FIG. 9 is a block diagram illustrating a configuration of a entanglement generation system according to a fourth embodiment. 10 is a flowchart illustrating an operation of the quantum entanglement generation system according to the fourth embodiment. The figure which compares and shows the relationship between the concurrence and success probability of a prior art, and the relationship between the concurrence and success probability in this invention.

  Hereinafter, embodiments of the present invention will be described in detail. In addition, the same number is attached | subjected to the structure part which has the same function, and duplication description is abbreviate | omitted. In this specification, the principle of the system of the present invention will be described on the assumption that all devices used in the transmission apparatus and the reception apparatus operate ideally. However, if the transmitter and receiver of a system are idealized and the system operating principle is found to be equivalent to the system operating principle described below, the system is equivalent to the present invention. Note that.

  Hereinafter, the quantum entanglement generation system according to the first embodiment will be described in detail with reference to FIGS. FIG. 4 is a block diagram showing the configuration of the entanglement generation system 1 of this embodiment. FIG. 5 is a flowchart showing the operation of the entanglement generation system 1 of the present embodiment. The quantum entanglement generation system 1 according to the present embodiment includes a transmission device 10, a reception device 20, and a transmission path 100. The transmission device 10 includes a qubit A81, a first interaction unit 82, a first displacement calculation unit 13, and a first switch 84. The first interaction unit 82 includes a beam splitter 82a. The first displacement calculation unit 13 includes a beam damper 13a, a beam splitter 13b, and a beam splitter 13c. The receiving device 20 includes a second switch 91, a qubit B92, a second interaction unit 93, a second displacement calculation unit 25, a detection light generation unit 94, a detection unit 96, and a determination unit 97. . The second interaction unit 93 includes a beam splitter 93a. The second displacement calculation unit 25 includes a beam damper 25a and a beam splitter 25b. The detection light generator 94 includes a beam splitter 94a. The detection unit 96 includes a photon detector 96a and a photon detector 96b.

First, the qubit A81 of the transmission apparatus 10 has α as an arbitrary real number satisfying α ≧ 0, ζ _α = (α ² sin θ) / 2, and T as a transmittance of the transmission line 100.

(S81). Here, the qubit A81 is realized by putting atoms into the resonator, and the initialization of the qubit A81 is realized by, for example, irradiating light with a wavelength corresponding to the energy gap of the atoms in the resonator. (See Appendix A). A desired state can be created by changing the light irradiation time. In the present invention, the method for realizing the qubit is only an example, and the method for realizing the qubit is not limited to the above. Further, the device for realizing the initialization is not essential in the present invention, so the details are omitted. The first interaction unit 82 irradiates the qubit A81 with an optical pulse μ whose amplitude and phase are expressed by α / √T, and through the unitary transformation ^ U expressed by the equation (4), quantum entanglement State

Is generated (S82). The optical pulse parameter α / √T can be realized by adjusting the reflectance of the beam splitter 82a. The unitary transformation {circumflex over (U)} in the equation (4) is realized, for example, by irradiating non-resonant light pulses to the atoms in the resonator constituting the qubit A81. The parameter θ depends on the degree of non-resonance between the atom and the incident light pulse, and the interaction strength / time, but the following discussion holds even if this degree of freedom is an arbitrary value. The expression (16) written as the output state of the unitary transformation ^ U is a mathematical expression of a synthetic system composed of a qubit A81 whose interaction has ended and an optical pulse μ coming out of this resonator after the interaction. is there. An example of how to implement unitary transformation ^ U is given in Appendix B.

  The first displacement calculator 13 applies a displacement operator to the optical pulse μ.

The state of the composite system is operated by operating the displacement calculator that realizes

Is generated (S13). Here, when the intense laser beam generated by the optical pulse μ and the beam splitter 13c is mixed by the beam splitter 13b having a very low reflectance, the displacement operator

Is obtained. Therefore, the beam splitter 13c that generates strong laser light and the beam splitter 13b with low reflectivity can be combined and regarded as one displacement calculation unit. The beam damper 13a is intended to discard unnecessary light. here,

-(Α / √T) cos (θ / 2), which can be controlled by adjusting the intensity of the laser beam incident on the beam splitter 13b.

Next, the first switch 84 transmits the optical pulse μ generated by the first displacement calculator 13 and the reference light LO to the receiving device 20 through the transmission line 100 (S84). Here, it is assumed that the first switch 84 can adjust the pulse path so that the optical pulse μ coming from different paths and the reference light LO run in parallel in the optical fiber. An optical pulse that has passed through the transmission line 100 is referred to as an optical pulse ν ₁ , E represents a state of the optical pulse that has leaked into the environmental system, and includes the environmental system after the optical pulse ν ₁ has passed through the transmission line 100. The state of the whole system is

It is represented by

The second switch 91 of the reception device 20 receives the reference light LO and the optical pulse ν ₁ from the transmission device 10 (S91). The qubit B92 is

(S92). Note that step S92 may be executed at any timing before, during, or after execution of steps S81, S82, S13, S84, and S91. Preparation and initialization of the qubit B92 can be realized by the same method as the qubit A81. The second interaction unit 93 generates β as an arbitrary real number satisfying β> α, generates an optical pulse ν ₂ whose amplitude and phase are represented by β from the reference light LO, and generates the optical pulse ν ₂ for the qubit B92. By irradiating the optical pulse ν ₂ , the unitary transformation ^ U expressed by the equation (4) is achieved, and the quantum entangled state

Is generated (S93). Here, the parameter β of the optical pulse ν ₂ can be adjusted by the reflectance of the beam splitter 93a.

The second displacement calculator 25 applies a displacement operator to the optical pulse ν _2.

The state of the composite system is operated by operating the displacement calculator that realizes

Generating an optical pulse [nu ₂ to form a (S25). The second displacement calculation unit 25 is configured based on the same principle as the displacement calculation executed by the first displacement calculation unit 13. However, the reflectivity of the beam splitter 25b of the second displacement calculation unit 25 needs to be set very high, and is different from the reflectivity of the beam splitter 13b of the first displacement calculation unit 13. But this is not an essential difference.

The detection light generation unit 94 receives the optical pulse ν ₁ and the optical pulse ν ₂ and inputs the optical pulse ν ₁ and the optical pulse ν ₂ .

An optical pulse ν ₃ and an optical pulse ν ₄ are generated by operating the beam splitter 94a which is a 50/50 beam splitter defined in (S94). Here, the right side of Expression (21) represents the state of the optical pulse ν ₃ and the optical pulse ν ₄ output from the beam splitter 94a. Further, the 50/50 beam splitter means a beam splitter having the characteristics that the reflectance and transmittance are 50% each. By this operation, the state of the whole system is

It becomes. This is a state corresponding to the expression (22 ′ ″).

Detector 96, the value depending on the number of photons of the optical pulse [nu _3, and a value dependent on the photon number of light pulses [nu ₄ measuring (S96). The determination unit 97 estimates whether there is a difference in the number of photons that the optical pulse ν ₃ and the optical pulse ν ₄ have, and determines a value depending on the number of photons of the measured optical pulse ν ₃ and the optical pulse ν ₄ . When it is estimated from the value depending on the number of photons that there is a difference in the number of photons held by the light pulse ν ₃ and the light pulse ν _4, it is determined that the quantum entanglement has been successfully shared, and the measured light pulse a value dependent on the number of photons [nu _3, when estimated from the values depending on the photon number of light pulses [nu ₄ as "no difference in the number of photons of light pulses [nu ₃ and the optical pulse [nu ₄ had" is It is determined that the quantum entanglement sharing has failed (S97). For example, the photon detector 96a measures the optical pulse ν ₃ , the photon detector 96b measures the optical pulse ν ₄ , and the determination unit 97 has a difference in the number of photons present in the optical pulse ν ₃ and the optical pulse ν _4. In this case, it can be realized by determining that the entanglement sharing is successful.

  Thus, the state of Expression (22) is configured by the entanglement generation system 1 of the present embodiment, which is substantially the same state as Expression (22 ′ ″). Therefore, the present entanglement generation system 1 is one embodiment of the present invention.

  The quantum entanglement generation system 1 according to the first embodiment is configured to include one displacement calculation unit (first displacement calculation unit 13 and second displacement calculation unit 25) in each of the transmission device 10 and the reception device 20. The positions of these displacement calculation units are variable, and can be collected on the receiving device side, for example. In the second embodiment, by integrating the displacement calculation unit on the reception device side, in addition to the effects of the first embodiment, the entanglement generation system 2 that can be used without changing the transmission device as a conventional transmission device. Will be described in detail with reference to FIGS. FIG. 6 is a block diagram showing the configuration of the entanglement generation system 2 of the present embodiment. FIG. 7 is a flowchart showing the operation of the entanglement generation system 2 of the present embodiment. The quantum entanglement generation system 2 of the present embodiment includes a transmission device 80, a reception device 30, and a transmission path 100. The transmission device 80 includes a qubit A81, a first interaction unit 82, and a first switch 84. The first interaction unit 82 includes a beam splitter 82a. The receiving device 30 includes a second switch 91, a qubit B92, a second interaction unit 93, a detection light generation unit 94, a second displacement calculation unit 38, a first displacement calculation unit 95, and a detection unit 96. And a determination unit 97. The second interaction unit 93 includes a beam splitter 93a. The detection light generator 94 includes a beam splitter 94a. The second displacement calculation unit 38 includes a beam splitter 38a, a beam splitter 38b, and a beam damper 38c. The first displacement calculation unit 95 includes a beam damper 95a and a beam splitter 95b. The detection unit 96 includes a photon detector 96a and a photon detector 96b.

In the qubit A81, α is α ≧ 0 and ζ _α = (α ² sin θ) / 2.

(S81). The first interaction unit 82 irradiates the qubit A81 with an optical pulse μ whose amplitude and phase are represented by α / √T (T is the transmittance of the transmission line 100), and the equation (4) Quantum entangled state through unitary transformation ^ U realized in

Is generated (S82).

The first switch 84 transmits the optical pulse μ and the reference light LO to the receiving device 30 through the transmission line 100 (S84). An optical pulse that has passed through the transmission line 100 is referred to as an optical pulse ν ₁ , E represents a state of the optical pulse that has leaked into the environmental system, and includes the environmental system after the optical pulse ν ₁ has passed through the transmission line 100. The state of the whole system is

It shall be represented by

The second switch 91 of the receiving device 30 receives the reference light LO and the optical pulse ν ₁ from the transmitting device 80 (S91). The qubit B92 has β as a real number satisfying β> α,

(S92). Note that step S92 may be executed at any timing before, during, or after steps S81, S82, S84, and S91. The second interaction portion 93, the amplitude and phase from the reference beam LO is to generate light pulses [nu ₂ represented by beta, to qubit B92, by irradiating the generated optical pulses [nu _2, entangled state

Is generated (S93).

The detection light generation unit 94 receives the optical pulse ν ₁ and the optical pulse ν ₂ as input, and the state of the entire system

To generate optical pulses ν ₃ and ν ₄ (S94). Similar to the first embodiment, the detection light generation unit 94 is realized by a 50/50 beam splitter 94a defined by Expression (21).

The second displacement calculator 38 applies a displacement operator to the optical pulse ν _3.

The optical pulse ν ₅ is formed by operating a displacement calculator (realized by the beam splitter 38a, the beam splitter 38b, and the beam damper 38c) that realizes (S38). The first displacement calculation unit 95 applies a displacement operator to the optical pulse ν _4.

The optical pulse ν ₆ is formed by applying a displacement calculator (realized by the beam damper 95a and the beam splitter 95b) that realizes (S95). The state of the entire system after the formation of the optical pulse ν ₅ and the optical pulse ν ₆ is

It shall be represented by This is a state corresponding to the expression (22 ′ ″).

Next, the detector 96 measures a value that depends on the number of photons of the optical pulse ν ₅ and a value that depends on the number of photons of the optical pulse ν ₆ (S96). Determining unit 97, whether there is a difference in the number of photons of light pulses [nu ₅ and the light pulse [nu ₆ had estimated, measured depending on the photon number of light pulses [nu ₅ values and the optical pulse [nu ₆ When it is estimated from the value depending on the number of photons that there is a difference in the number of photons held by the light pulse ν ₅ and the light pulse ν _6, it is determined that the quantum entanglement has been successfully shared, and the measured light pulse a value dependent on the number of photons [nu _5, when estimated from the values depending on the photon number of light pulses [nu ₆ as "no difference in the number of photons of light pulses [nu ₅ and the light pulse [nu ₆ had" is It is determined that the quantum entanglement sharing has failed (S97).

  As described above, according to the quantum entanglement generation system 2 of the present embodiment, in addition to the effects of the first embodiment, the displacement calculation functions are concentrated on the receiving device 30 side. It is possible to realize quantum entanglement with an efficiency close to the theoretical limit when the error is not limited.

  In the quantum entanglement generation system 1 according to the first embodiment, each of the transmission device 10 and the reception device 20 has a displacement calculation function. In the quantum entanglement generation system 2 according to the second embodiment, the displacement calculation function is integrated on the reception device 30 side. did. However, as described above, the essence of the present invention is to prepare the quantum entangled state expressed by the equation (22 '' '), and it is not an important problem where the displacement calculation or the like is performed. Therefore, the configuration pattern of the displacement calculation function capable of achieving the object of the present invention is not limited to the first and second embodiments, and other patterns can be considered. Therefore, in Example 3 and Example 4 to be described later, a system in which elements necessary for achieving the object of the present invention are abstracted as all the high-level concepts such as the configuration patterns of these displacement calculation functions. An example will be described. First, the quantum entanglement generation system 3 will be described in detail with reference to FIGS. FIG. 8 is a block diagram showing the configuration of the entanglement generation system 3 of this embodiment. FIG. 9 is a flowchart showing the operation of the entanglement generation system 3 of the present embodiment. The quantum entanglement generation system 3 according to the present embodiment includes a transmission device 40, a reception device 50, and a transmission path 100. The transmission device 40 includes a qubit A41, a first interaction unit 42, and a first switch 44. The receiving device 50 includes a second switch 51, a qubit B52, a second interaction unit 53, a detection light generation unit 54, a detection unit 56, and a determination unit 57. The first interaction unit 42, the second interaction unit 53, and the detection light generation unit 54 can be realized by a light generation mechanism, a beam splitter, a shooter, and the like. Any configuration that has an executable function is acceptable. The detection unit 56 can be realized by an arbitrary photon detector as described in the first and second embodiments.

  First, qubit A41 is

(S41). The first interaction unit 42 irradiates the qubit A41 with an optical pulse μ, and sets α ₀ as a complex number representing the amplitude and phase of coherent light corresponding to a state where the qubit A41 is ₀ , and the qubit A41 is 1 the complex number representing the amplitude and phase of the coherent light corresponding to the state as alpha _1, entangled state

Is generated (S42).

  The first switch 44 uses T as the transmittance of the transmission line 100, and the quantum entangled state

And the reference light LO are transmitted to the receiving device 50 through the transmission line 100 (S44). An optical pulse that has passed through the transmission line 100 is referred to as an optical pulse ν ₁ , E represents a state of the optical pulse that has leaked into the environmental system, and includes the environmental system after the optical pulse ν ₁ has passed through the transmission line 100. The state of the whole system is

It shall be represented by

The second switch 51 of the receiving device 50 receives the reference light LO and the optical pulse ν ₁ from the transmitting device 40 (S51). The qubit B52 is

(S52). Note that step S52 may be executed at any timing before, during, or after execution of steps S41, S42, S44, and S51. The second interaction unit 53 generates an optical pulse ν ₂ from the reference light LO, irradiates the qubit B 52 with the generated optical pulse ν _2, and coherent light corresponding to a state in which the qubit B 52 is 0. Quantum entangled state, where β ₀ is a complex number representing the amplitude and phase of the light and β ₁ is a complex number representing the amplitude and phase of coherent light corresponding to the state where qubit B52 is 1.

Is generated (S53).

The detection light generation unit 54 receives the optical pulse ν ₁ and the optical pulse ν ₂ and inputs the state of the entire system.

(Where a: = | α ₀ −α ₁ | / 2, b: = | β ₀ −β ₁ | / 2 is an arbitrary real number satisfying a ≠ b, and θ ₀ , θ ₁ , θ _p , θ _q Are generated as optical pulses ν ₃ and ν ₄ (S54).

Detector 56, the value depending on the number of photons of the optical pulse [nu _3, and a value dependent on the photon number of light pulses [nu ₄ measuring (S56). Determining unit 57, whether there is a difference in the number of photons of light pulses [nu ₃ and the optical pulse [nu ₄ had estimated, measured values depending on the number of photons of the optical pulse [nu ₃ and the optical pulse [nu ₄ When it is estimated from the value depending on the number of photons that there is a difference in the number of photons held by the light pulse ν ₃ and the light pulse ν _4, it is determined that the quantum entanglement has been successfully shared, and the measured light pulse a value dependent on the number of photons [nu _3, when estimated from the values depending on the photon number of light pulses [nu ₄ as "no difference in the number of photons of light pulses [nu ₃ and the optical pulse [nu ₄ had" is It is determined that the quantum entanglement sharing has failed (S57).

  The method shown here corresponds to the superordinate concept of the first and second embodiments. Further, setting a ≠ b in the equation (22 ′ ″) leads to no limitation on the type of generated quantum entanglement error. As a result, the present embodiment has an efficiency close to the theoretical limit (13). Can be achieved.

The first entanglement generation unit 65 represents α ₀ as a complex number representing the amplitude and phase of coherent light corresponding to the state where the qubit A41 is 0, and represents the amplitude and phase of coherent light corresponding to the state where the qubit A41 is 1. entangled state of a complex number as alpha _1, qubit A41 and the light pulse μ

And the optical pulse μ is transmitted through the transmission line 110 (transmittance T) (S65). The optical pulse that has passed through the transmission path 110 is referred to as an optical pulse ν _1, and E represents the state of the optical pulse that has leaked into the environmental system, including the environmental system after the optical pulse ν ₁ has passed through the transmission path 110. The state of the whole system is

It becomes.

Second entangled generator 79 represents the coherent light amplitude and phase qubit B52 is ₀ the complex β representing the coherent light amplitude and phase corresponding to the state of _0, qubits B52 corresponds to one state Quantum entangled state of qubit B52 and optical pulse ν ₂ with complex number β ₁

Is generated (S79). Note that step S79 may be executed at any timing before, during, or after execution of step S65. The detection light generation unit 54 receives the optical pulse ν ₁ and the optical pulse ν ₂ and inputs the state of the entire system.

(Where a: = | α ₀ −α ₁ | / 2, b: = | β ₀ −β ₁ | / 2 is an arbitrary real number satisfying a ≠ b, and θ ₀ , θ ₁ , θ _p , θ _q Are generated as optical pulses ν ₃ and ν ₄ (S54). Detector 56, the value depending on the number of photons of the optical pulse [nu _3, and a value dependent on the photon number of light pulses [nu ₄ measuring (S56). Determining unit 57, the measured difference in the number of photons "light pulses [nu ₃ and the optical pulse [nu ₄ had a value dependent on the number of photons of the photon number-dependent value and the optical pulse [nu ₄ light pulses [nu ₃ If it is presumed that the quantum entanglement was successfully shared, the value depending on the number of photons of the measured light pulse ν ₃ and the value depending on the number of photons of the light pulse ν ₄ If it is presumed that there is no difference in the number of photons possessed by the optical pulse ν ₃ and the optical pulse ν _4, it is determined that sharing of the entanglement has failed (S57).

  The method shown here corresponds to the superordinate concept of the first, second, and third embodiments. Further, setting a ≠ b in the equation (22 ′ ″) leads to no limitation on the type of generated quantum entanglement error. As a result, the present embodiment has an efficiency close to the theoretical limit (13). Can be achieved.

<Appendix A: Qubits>
A qubit takes two different states {| 0>, | 1>} and is generally a superposition state.

Take. However, α and β are complex numbers satisfying | α | ² + | β | ² = 1. Basically, it is required that three operations “initialization, 1 qubit unitary operation, and measurement” can be realized for a qubit. Initialization refers to the ability to freely select the complex coefficients α and β in equation (26). Unitary operation

Is a three-dimensional unit vector ( _nx , _ny , _nz ) and a Pauli operator

Using,

Written and state

Convert to The measurement also determines whether the qubit is in the state of | 0> or | 1>. For example, by performing measurements on condition that the equation (26), the probability | alpha ^{| 2} by | 0>, the probability | is determined 1> is in the state that the | beta ^{| 2} in. There are various examples of such qubits. For example, single photons, superconducting qubits, quantum dots, NV centers in diamond, atoms, ions, etc. can be used as qubits. The specific “initialization, 1 qubit unitary calculation, measurement” implementation method differs for each physical system. For example, when the energy eigenstates {| e>, | g>} of an atom are made to correspond to {| 0>, | 1>} of qubits, these basic operations are performed by applying laser light of an appropriate frequency. It is known that this can be achieved by irradiating atoms for the time.

<Appendix B: Example of how to realize interaction ^ U>
Here, an example of a method for realizing ^ U will be described. An energy eigenstate {| e>, | g>} of a certain two-level system (for example, a single atom) is made to correspond to {| 0>, | 1>} of qubits. The assumption for obtaining the interaction ^ U is
(1) The interaction between the two-level system and light is the Jaynes-Cummings Hamiltonian

(Ω: frequency of light, −hω: energy difference of two-level system, Ω: Rabi frequency, ^ σ ₊ : = | g><e |, ^ σ ₋ : = | e><g |, ^ (2) What is described in (a) Light extinction operator) (2) Non-resonant (| ω−ω ′ | >> Ω) irradiation with laser light. Assumption 1 is that superconducting qubits, quantum dots, NV centers in diamond,
Satisfied with almost all physical systems such as atoms and ions. Assumption 2 only needs to prepare a laser that satisfies the required conditions. At this time, θ appearing in the equation (4) can be expressed as follows, where the interaction time is t.

Determined by In a typical physical system such as a quantum dot, it is expected that θ to 0.01 can be achieved (see Non-Patent Document 2).

Claims (8)

A quantum entanglement generation system comprising: a transmission device; a transmission line having a transmittance T that can cancel a phase change received by an optical pulse during transmission; and a reception device,
The transmitter is
Qubit A;
The complex number representing the amplitude and phase of coherent light corresponding to the state where the qubit A is 0 is α ₀ , and the complex number representing the amplitude and phase of coherent light corresponding to the state where the qubit A is 1 is α _1. Quantum entangled state of A and light pulse μ

And a first quantum entanglement generator that transmits the optical pulse μ through the transmission line,
The optical pulse that has passed through the transmission path is referred to as an optical pulse ν ₁ , E represents the state of the optical pulse that has leaked into the environmental system, and includes all environmental systems after the optical pulse ν ₁ has passed through the transmission path. The state of the system is

It shall be represented by
The receiving device is:
Qubit B;
The complex number representing the amplitude and phase of the coherent light corresponding to the state where the qubit B is 0 is β ₀ , and the complex number representing the amplitude and phase of the coherent light corresponding to the state where the qubit B is 1 is β _1. Quantum entangled state of B and light pulse ν ₂

A second entanglement generator for generating
The state of the whole system with light pulse ν ₁ and light pulse ν ₂ as inputs

(Where a: = | α ₀ −α ₁ | / 2, b: = | β ₀ −β ₁ | / 2 is an arbitrary real number satisfying a ≠ b, and θ ₀ , θ ₁ , θ _p , θ _q A detection light generation unit that generates optical pulses ν ₃ and ν ₄ that form an arbitrary real number),
A detection unit for measuring a value dependent on the number of photons of the optical pulse [nu _3, and depending on the number of photons of the optical pulse [nu ₄ values,
It is estimated whether or not there is a difference between the number of photons of the light pulse ν ₃ and the light pulse ν ₄ measured in the previous period, and the value depending on the number of photons of the measured light pulse ν _{3 and} the photon of the light pulse ν ₄ . If it is estimated from the value depending on the number that there is a difference in the number of photons held by the optical pulse ν ₃ and the optical pulse ν _4, it is determined that the sharing of the quantum entanglement is successful, and the measured optical pulse ν ₃ and the value dependent on the number of photons of the optical pulse ν ₄ , it is estimated that “there is no difference in the number of photons of the optical pulse ν ₃ and the optical pulse ν ₄ ”. A determination unit that determines that sharing of the tangle has failed;
A entanglement generating system characterized by comprising: A quantum entanglement generation system including a transmission device and a reception device,
The transmitter is

A qubit A initialized to
When the qubit A is irradiated with an optical pulse μ, the complex number representing the amplitude and phase of the coherent light corresponding to the state where the qubit A is 0 is α ₀ , and the coherent light corresponding to the state where the qubit A is 1 Quantum entangled state, where α ₁ is the complex number representing the amplitude and phase of

A first interaction unit for generating
Let T be the transmission rate of the transmission line, the reference light LO and the entangled state

A first switch that transmits the optical pulse μ forming the signal to the receiving device through the transmission path,
The optical pulse that has passed through the transmission path is referred to as an optical pulse ν ₁ , E represents the state of the optical pulse that has leaked into the environmental system, and includes all environmental systems after the optical pulse ν ₁ has passed through the transmission path. The state of the system is

It shall be represented by
The receiving device
A second switch for receiving the reference light LO and the optical pulse ν ₁ from a transmission device;

A qubit B initialized to
An optical pulse ν ₂ is generated from the reference light LO, the generated optical pulse ν ₂ is irradiated to the qubit B, and the amplitude and phase of the coherent light corresponding to the state where the qubit B is 0 is obtained. complex beta _0, a ₁ complex beta representing the coherent light amplitude and phase of the qubit B corresponds to one state, entangled state indicating

A second interaction unit for generating
The optical pulse ν ₁ and the optical pulse ν ₂ are input, and the state of the entire system

(Where a: = | α ₀ −α ₁ | / 2, b: = | β ₀ −β ₁ | / 2 is an arbitrary real number satisfying a ≠ b, and θ ₀ , θ ₁ , θ _p , θ _q A detection light generation unit that generates optical pulses ν ₃ and ν ₄ that form an arbitrary real number),
A detection unit for measuring a value dependent on the number of photons of the optical pulse [nu _3, and depending on the number of photons of the optical pulse [nu ₄ values,
It is estimated whether or not there is a difference between the number of photons of the light pulse ν ₃ and the light pulse ν ₄ measured in the previous period, and the value depending on the number of photons of the measured light pulse ν _{3 and} the photon of the light pulse ν ₄ . If it is estimated from the value depending on the number that there is a difference in the number of photons held by the optical pulse ν ₃ and the optical pulse ν _4, it is determined that the sharing of the quantum entanglement is successful, and the measured optical pulse ν ₃ and the value dependent on the number of photons of the optical pulse ν ₄ , it is estimated that “there is no difference in the number of photons of the optical pulse ν ₃ and the optical pulse ν ₄ ”. A determination unit that determines that sharing of the tangle has failed;
A entanglement generating system characterized by comprising: A quantum entanglement generation system including a transmission device and a reception device,
The transmission device is an arbitrary real number satisfying α ≧ 0, ζ _α = (α ² sin θ) / 2, and T is a transmission path transmittance.

A qubit A initialized to
The quantum bit A is irradiated with an optical pulse μ whose amplitude and phase are represented by a complex number α / √T, and a quantum entangled state

A first interaction unit for generating
A displacement operator is applied to the light pulse μ.

The state of the composite system is operated by operating the displacement calculator that realizes

A first displacement calculator that generates an optical pulse μ forming
A first switch that transmits the optical pulse μ and the reference light LO generated by the first displacement calculation unit to the receiving device through the transmission path;
The optical pulse that has passed through the transmission path is referred to as an optical pulse ν ₁ , E represents the state of the optical pulse that has leaked into the environmental system, and includes all environmental systems after the optical pulse ν ₁ has passed through the transmission path. The state of the system is

It shall be represented by
The receiving device
A second switch for receiving the reference light LO and the optical pulse ν ₁ from a transmission device;
Let β be any real number satisfying β> α,

A qubit B initialized to
An optical pulse ν ₂ whose amplitude and phase are represented by a complex number β is generated from the reference light LO, and the generated optical pulse ν ₂ is irradiated to the qubit B, so that a entangled state

A second interaction unit for generating
A displacement operator is applied to the light pulse ν _2.

The state of the composite system is operated by operating the displacement calculator that realizes

A second displacement calculator that generates an optical pulse ν ₂ forming
The optical pulse ν ₁ and the optical pulse ν ₂ are input, and the state of the entire system

A detection light generator that generates optical pulses ν ₃ and ν ₄ that form
A detection unit for measuring a value dependent on the number of photons of the optical pulse [nu _3, and depending on the number of photons of the optical pulse [nu ₄ values,
It is estimated whether or not there is a difference between the number of photons of the light pulse ν ₃ and the light pulse ν ₄ measured in the previous period, and the value depending on the number of photons of the measured light pulse ν _{3 and} the photon of the light pulse ν ₄ . If it is estimated from the value depending on the number that there is a difference in the number of photons held by the optical pulse ν ₃ and the optical pulse ν _4, it is determined that the sharing of the quantum entanglement is successful, and the measured optical pulse ν ₃ and the value dependent on the number of photons of the optical pulse ν ₄ , it is estimated that “there is no difference in the number of photons of the optical pulse ν ₃ and the optical pulse ν ₄ ”. A determination unit that determines that sharing of the tangle has failed;
A entanglement generating system characterized by comprising: A quantum entanglement generation system including a transmission device and a reception device,
The transmission device can be defined as any real number satisfying α ≧ 0, ζ _α = (α ² sin θ) / 2.

A qubit A initialized to
The quantum bit A is irradiated with an optical pulse μ whose amplitude and phase are represented by a complex number α / √T (where T is the transmittance of the transmission line), and the quantum entangled state

A first interaction unit for generating
A first switch that transmits the optical pulse μ and the reference light LO to the receiving device through the transmission path;
The optical pulse that has passed through the transmission path is referred to as an optical pulse ν ₁ , E represents the state of the optical pulse that has leaked into the environmental system, and includes all environmental systems after the optical pulse ν ₁ has passed through the transmission path. The state of the system is

It shall be represented by
The receiving device
A second switch for receiving the reference light LO and the optical pulse ν ₁ from a transmission device;
Let β be any real number satisfying β> α,

A qubit B initialized to
An optical pulse ν ₂ whose amplitude and phase are represented by a complex number β is generated from the reference light LO, and the generated optical pulse ν ₂ is irradiated to the qubit B, so that a entangled state

A second interaction unit for generating
The optical pulse ν ₁ and the optical pulse ν ₂ are input, and the state of the entire system

A detection light generator that generates optical pulses ν ₃ and ν ₄ that form
A displacement operator is applied to the light pulse ν _3.

A second displacement calculator that forms a light pulse ν ₅ by operating a displacement calculator that realizes
A displacement operator is applied to the light pulse ν _4.

A first displacement calculator that forms a light pulse ν ₆ by operating a displacement calculator that realizes
The state of the entire system after the formation of the light pulse ν ₅ and the light pulse ν ₆ is

It shall be represented by
A detector for measuring a value depending on the number of photons of the light pulse ν ₅ and a value depending on the number of photons of the light pulse ν ₆ ;
It is estimated whether there is a difference between the number of photons of the optical pulse ν ₅ and the optical pulse ν ₆ measured in the previous period, and the value depending on the number of photons of the measured optical pulse ν _{5 and} the photon of the optical pulse ν ₆ . If it is estimated from the value depending on the number that there is a difference in the number of photons held by the light pulse ν ₅ and the light pulse ν _6, it is determined that the sharing of the quantum entanglement is successful, and the measured light pulse ν a value dependent on the number of photons of _5, when estimated from the values depending on the photon number of light pulses [nu ₆ as "no difference in the number of photons of light pulses [nu ₅ and the light pulse [nu ₆ had" is a quantum A determination unit that determines that sharing of the tangle has failed;
A entanglement generating system characterized by comprising: A quantum entanglement generation method using a transmission device, a transmission line having a transmittance T capable of canceling a phase change received by an optical pulse during transmission, and a reception device,
The transmitter is
The complex number representing the amplitude and phase of the coherent light corresponding to the state where the qubit A is 0 is α ₀ , and the complex number representing the amplitude and phase of the coherent light corresponding to the state where the qubit A is 1 is α _1. And entangled state of light pulse μ

And generating a first entanglement generating step of transmitting the optical pulse μ through the transmission line,
The optical pulse that has passed through the transmission path is referred to as an optical pulse ν ₁ , E represents the state of the optical pulse that has leaked into the environmental system, and includes all environmental systems after the optical pulse ν ₁ has passed through the transmission path. The state of the system is

It shall be represented by
The receiving device is:
A complex number representing the amplitude and phase of coherent light corresponding to the state where the qubit B is 0 is β ₀ , and a complex number representing the amplitude and phase of coherent light corresponding to the state where the qubit B is 1 is β ₁ , and the qubit B And entangled state of light pulse ν ₂

A second entanglement generating step for generating
The state of the whole system with light pulse ν ₁ and light pulse ν ₂ as inputs

(Where a: = | α ₀ −α ₁ | / 2, b: = | β ₀ −β ₁ | / 2 is an arbitrary real number satisfying a ≠ b, and θ ₀ , θ ₁ , θ _p , θ _q A detection light generation step for generating optical pulses ν ₃ and ν ₄ that form an arbitrary real number),
A detection step of measuring a value dependent on the number of photons of the optical pulse [nu _3, and depending on the number of photons of the optical pulse [nu ₄ values,
It is estimated whether or not there is a difference between the number of photons of the light pulse ν ₃ and the light pulse ν ₄ measured in the previous period, and the value depending on the number of photons of the measured light pulse ν _{3 and} the photon of the light pulse ν ₄ . If it is estimated from the value depending on the number that there is a difference in the number of photons held by the optical pulse ν ₃ and the optical pulse ν _4, it is determined that the sharing of the quantum entanglement is successful, and the measured optical pulse ν ₃ and the value dependent on the number of photons of the optical pulse ν ₄ , it is estimated that “there is no difference in the number of photons of the optical pulse ν ₃ and the optical pulse ν ₄ ”. A determination step for determining that sharing of the tangle has failed;
Quantum entanglement generation method characterized by performing A quantum entanglement generation method using a transmission device and a reception device,
The transmitter is
The qubit A is

A first initialization step to initialize to
When the qubit A is irradiated with an optical pulse μ, the complex number representing the amplitude and phase of the coherent light corresponding to the state where the qubit A is 0 is α ₀ , and the coherent light corresponding to the state where the qubit A is 1 Quantum entangled state, where α ₁ is the complex number representing the amplitude and phase of

A first interaction step for generating
Let T be the transmission rate of the transmission line, the reference light LO and the entangled state

And a first switch step of transmitting the optical pulse μ forming the receiver to the receiving device through the transmission path,
The optical pulse that has passed through the transmission path is referred to as an optical pulse ν ₁ , E represents the state of the optical pulse that has leaked into the environmental system, and includes all environmental systems after the optical pulse ν ₁ has passed through the transmission path. The state of the system is

It shall be represented by
The receiving device
A second switch step for receiving the reference light LO and the optical pulse ν ₁ from a transmitter;
The qubit B is

A second initialization step to initialize to
An optical pulse ν ₂ is generated from the reference light LO, the generated optical pulse ν ₂ is irradiated to the qubit B, and the amplitude and phase of the coherent light corresponding to the state where the qubit B is 0 is obtained. complex beta _0, a ₁ complex beta representing the coherent light amplitude and phase of the qubit B corresponds to one state, entangled state indicating

A second interaction step for generating
The optical pulse ν ₁ and the optical pulse ν ₂ are input, and the state of the entire system

(Where a: = | α ₀ −α ₁ | / 2, b: = | β ₀ −β ₁ | / 2 is an arbitrary real number satisfying a ≠ b, and θ ₀ , θ ₁ , θ _p , θ _q A detection light generation step for generating optical pulses ν ₃ and ν ₄ that form an arbitrary real number),
A detection step of measuring a value dependent on the number of photons of the optical pulse [nu _3, and depending on the number of photons of the optical pulse [nu ₄ values,
It is estimated whether or not there is a difference between the number of photons of the light pulse ν ₃ and the light pulse ν ₄ measured in the previous period, and the value depending on the number of photons of the measured light pulse ν _{3 and} the photon of the light pulse ν ₄ . If it is estimated from the value depending on the number that there is a difference in the number of photons held by the optical pulse ν ₃ and the optical pulse ν _4, it is determined that the sharing of the quantum entanglement is successful, and the measured optical pulse ν ₃ and the value dependent on the number of photons of the optical pulse ν ₄ , it is estimated that “there is no difference in the number of photons of the optical pulse ν ₃ and the optical pulse ν ₄ ”. A determination step for determining that sharing of the tangle has failed;
Quantum entanglement generation method characterized by performing A quantum entanglement generation method comprising a transmission device and a reception device,
The transmitter is
Quantum bit A, α is an arbitrary real number satisfying α ≧ 0, ζ _α = (α ² sin θ) / 2, and T is a transmission path transmittance.

A first initialization step to initialize to
The quantum bit A is irradiated with an optical pulse μ whose amplitude and phase are represented by a complex number α / √T, and a quantum entangled state

A first interaction step for generating
A displacement operator is applied to the light pulse μ.

The state of the composite system is operated by operating the displacement calculator that realizes

A first displacement calculation step for generating an optical pulse μ forming
Performing a first switch step of transmitting the optical pulse μ and the reference light LO generated in the first displacement calculation step to the receiving device through the transmission path;
The optical pulse that has passed through the transmission path is referred to as an optical pulse ν ₁ , E represents the state of the optical pulse that has leaked into the environmental system, and includes all environmental systems after the optical pulse ν ₁ has passed through the transmission path. The state of the system is

It shall be represented by
The receiving device
A second switch step for receiving the reference light LO and the optical pulse ν ₁ from a transmitter;
Let qubit B be an arbitrary real number satisfying β> α, β

A second initialization step to initialize to
An optical pulse ν ₂ whose amplitude and phase are represented by a complex number β is generated from the reference light LO, and the generated optical pulse ν ₂ is irradiated to the qubit B, so that a entangled state

A second interaction step for generating
A displacement operator is applied to the light pulse ν _2.

The state of the composite system is operated by operating the displacement calculator that realizes

A second displacement calculating step for generating an optical pulse ν ₂ forming
The optical pulse ν ₁ and the optical pulse ν ₂ are input, and the state of the entire system

A detection light generation step for generating optical pulses ν ₃ and ν ₄ to form
A detection step of measuring a value dependent on the number of photons of the optical pulse [nu _3, and depending on the number of photons of the optical pulse [nu ₄ values,
It is estimated whether or not there is a difference between the number of photons of the light pulse ν ₃ and the light pulse ν ₄ measured in the previous period, and the value depending on the number of photons of the measured light pulse ν _{3 and} the photon of the light pulse ν ₄ . If it is estimated from the value depending on the number that there is a difference in the number of photons held by the optical pulse ν ₃ and the optical pulse ν _4, it is determined that the sharing of the quantum entanglement is successful, and the measured optical pulse ν ₃ and the value dependent on the number of photons of the optical pulse ν ₄ , it is estimated that “there is no difference in the number of photons of the optical pulse ν ₃ and the optical pulse ν ₄ ”. A determination step for determining that sharing of the tangle has failed;
Quantum entanglement generation method characterized by performing A quantum entanglement generation method using a transmission device and a reception device,
The transmitter is
For qubit A, α is an arbitrary real number satisfying α ≧ 0, ζ _α = (α ² sin θ) / 2,

A first initialization step to initialize to
The quantum bit A is irradiated with an optical pulse μ whose amplitude and phase are represented by a complex number α / √T (where T is the transmittance of the transmission line), and the quantum entangled state

A first interaction step for generating
Performing a first switch step of transmitting the optical pulse μ and the reference light LO to the receiving device through the transmission path;
The optical pulse that has passed through the transmission path is referred to as an optical pulse ν ₁ , E represents the state of the optical pulse that has leaked into the environmental system, and includes all environmental systems after the optical pulse ν ₁ has passed through the transmission path. The state of the system is

It shall be represented by
The receiving device
A second switch step for receiving the reference light LO and the optical pulse ν ₁ from a transmitter;
Let qubit B be an arbitrary real number satisfying β> α, β

A second initialization step to initialize to
An optical pulse ν ₂ whose amplitude and phase are represented by a complex number β is generated from the reference light LO, and the generated optical pulse ν ₂ is irradiated to the qubit B, so that a entangled state

A second interaction step for generating
The optical pulse ν ₁ and the optical pulse ν ₂ are input, and the state of the entire system

A detection light generation step for generating optical pulses ν ₃ and ν ₄ to form
A displacement operator is applied to the light pulse ν _3.

A second displacement calculating step of forming a light pulse ν ₅ by operating a displacement calculator for realizing
A displacement operator is applied to the light pulse ν _4.

A first displacement calculation step of forming a light pulse ν ₆ by operating a displacement calculator for realizing
The state of the entire system after the formation of the light pulse ν ₅ and the light pulse ν ₆ is

It shall be represented by
A detection step of measuring a value depending on the number of photons of the light pulse ν ₅ and a value depending on the number of photons of the light pulse ν ₆ ;
It is estimated whether there is a difference between the number of photons of the optical pulse ν ₅ and the optical pulse ν ₆ measured in the previous period, and the value depending on the number of photons of the measured optical pulse ν _{5 and} the photon of the optical pulse ν ₆ . If it is estimated from the value depending on the number that there is a difference in the number of photons held by the light pulse ν ₅ and the light pulse ν _6, it is determined that the sharing of the quantum entanglement is successful, and the measured light pulse ν a value dependent on the number of photons of _5, when estimated from the values depending on the photon number of light pulses [nu ₆ as "no difference in the number of photons of light pulses [nu ₅ and the light pulse [nu ₆ had" is a quantum A determination step for determining that sharing of the tangle has failed;
A method for generating entanglement, comprising:

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