JP4460362B2 - Quantum state generation method and center apparatus for quantum state generation - Google Patents

Description

  The present invention relates to a quantum state generation method for generating a quantum state, a quantum state generation center device, and a quantum state generation program thereof, and in particular, a quantum state is generated by cooperation of devices having a secret sharing value or higher than a threshold value. The present invention relates to a quantum state generation method, a quantum state generation center device, and a quantum state generation program thereof.

Conventionally, a method called “distributed encryption method” or “threshold encryption method” has been proposed for encryption processing (Y. Desmedt and Y. Frankel, “Threshold Cryptosystems”, Proc. Of Crypto '89, pp. 307-315, LNCS, Springer-Verlag (1990)). This scheme, a secret key s of the plurality of information s _1, ..., distributed s _m, keep a these shared information s _i to each center apparatus P _i. Then, an arbitrary k number of center devices cooperate to realize a process equivalent to the process using the secret key s. Thereby, the process using the secret key s can be executed without the secret key s being known to each center apparatus.

In addition, in quantum cryptography and quantum cash processing, a quantum state based on secret information is generated. In Non-Patent Documents 1 and 2, a “distributed cryptosystem” that can be applied to secret information using such a quantum state. And “threshold cryptography” have also been proposed. In this method, first, one center device once holds the secret information K, distributes the distributed information _Sq to each center device, and then the center devices above the threshold value cooperate with the secret information K. Generate quantum states.
Japanese Patent Laid-Open No. 2004-32520 JP 2004-32521 A

However, in the case of the methods of Non-Patent Documents 1 and 2, since one center device (distributor) knows all secret information, there is a way to prevent fraud such as leakage or falsification of secret information of this center device. There is no problem.
The present invention has been made in view of the above points, and provides a technique capable of generating a quantum state corresponding to secret information without any center device knowing the entire secret information. The purpose is to do.

In the present invention, in order to solve the above problems, first, the secret value generation unit of each quantum state generation center device P _j (jε {1, 2,..., N}, n ≧ 2) σ _j = {(a _{j, 1} , b _{j, 1} ), (a _{j, 2} , b _{j, 2} ),..., (a _{j, m} , b _{j, m} )} (a _{j, i} ∈ {0 _{, 1}, b j, i} ∈ {0,1}, i∈ {1,2, ..., m}, m generates a natural number), the secret distribution unit, the dispersion value _{S j} private value sigma _{j, q} (qε {1, 2,..., n}) is generated, and the classical transmission unit secretly transmits the dispersion value S _{j, q} to the quantum state generation center device _Pq . Further, the classical reception unit of each quantum state generation center device P _j receives the dispersion value S _{q, j} transmitted from the other quantum state generation center device P _q .

を満たす補完値Ｋ^［ｒ］＝｛（ａ_１ ^［ｒ］，ｂ_１ ^［ｒ］），（ａ_２ ^［ｒ］，ｂ_２ ^［ｒ］），…，（ａ_ｍ ^［ｒ］，ｂ_ｍ ^［ｒ］）｝（ａ_ｉ ^［ｒ］∈｛０，１｝、ｂ_ｉ ^［ｒ］∈｛０，１｝、ｉ∈｛１，２，…，ｍ｝）を、それぞれ算出する。 Next, t (2 ≦ t ≦ n) each of the quantum state generating center devices P _r (rε {1, 2,..., T}) does not know the entire secret information K, Exclusive OR from variance values S _{q, r}

Complementary value ^K which satisfies the _{^{[r] = {(a 1}} [r], b 1 [r]), (a 2 [r], b 2 [r]), ..., (a m [r], b m [ ^r] )} (a _i ^[r] ∈ {0, 1}, b _i ^[r] ∈ {0, 1}, _i ∈ {1, 2,..., m}).

を生成し、量子送信部が、この量子状態｜φ^［１］＞を量子状態生成用センター装置Ｐ_２に送信する。 Then, the quantum state generating unit of the quantum state generating center device P ₁ is, quantum state

Generates, quantum transmitting unit, the quantum state | send phi ^[1]> the quantum state generating center device P _2.

を施し、その結果である量子状態｜φ^［ｓ］＞を量子送信部が送信する、といった処理を繰り返す。 Thereafter, the quantum state generating center apparatus _{P s (s∈ {2, ...} , t}) quantum receiving unit of quantum state transmitted from the quantum state generating center apparatus ^{_{P s-1 | φ [s}} -1] > And the unitary transform unit transforms the unitary transform for the quantum state | φ ^[s-1] >.

And the quantum transmission unit transmits the resulting quantum state | φ ^[s] >.

Here, the finally generated quantum state | φ ^[t] > is a quantum state indicating the entire secret information K. Each quantum state generation center device P _j generates each quantum state from the secret value σ _j generated by itself and the distributed value of the secret value transmitted from the other quantum state generation center devices. The whole secret information K does not leak to any quantum state generating center device.

  As described above, in the present invention, the quantum state corresponding to the secret information can be generated without any quantum state generating center device knowing the entire secret information.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
〔Overview〕
In this embodiment, each quantum state generation center device (P _j ) (j∈ {1, 2,..., N}) uses the secret sharing method to distribute the distributed values S _{j, q} from the respective secret values σ _j. (Qε {1, 2,... N}) are generated, and these are delivered one by one to other quantum state generating center devices (P _q ). Then, t quantum state generation center devices (2 ≦ t ≦ n) cooperate to sequentially generate quantum information related to the dispersion value, and finally, the total secret value σ _j (j Quantum information corresponding to the entire secret information K determined by ∈ {1, 2,..., N}) is generated.

〔System configuration〕
FIG. 1 is a diagram showing an overall configuration of a quantum state generation system 1 in the present embodiment.
The quantum state generation system 1 of this example includes n (n ≧ 2) quantum state generation center devices 10-1 (P ₁ ) to 10-n (P _n ), which are the classical communication channel 30 and The quantum communication path 40 is configured to be able to communicate with each other. In FIGS. 1 to 5, solid arrows indicate the flow of quantum information, and broken arrows indicate the flow of classical information.
[Configuration of center device for quantum state generation]
Next, the configuration of the quantum state generating center device in this embodiment will be described.

<Common configuration>
FIG. 2 is a block diagram showing a functional configuration that all the quantum state generating center devices 10 (“10-1 (P ₁ ) to 10-n (P _n )”) of this example have in common.
As illustrated in FIG. 2, each quantum state generation center device 10 includes a random value generation unit 11, a secret value generation unit 12, a secret sharing unit 13, a classic transmission unit 14, a classic reception unit 15, and a memory 16. The classical transmission unit 14 and the classical reception unit 15 are connected to the classical communication path 30 so as to be communicable.

<Structure of _{P 1>}
FIG. 3 is a block diagram illustrating functions of the quantum state generation center device 10-1 (P ₁ ). The quantum state generation center device 10-1 (P ₁ ) includes t (2 ≦ t ≦ n) quantum state generation center devices (P _r : r) selected from all the quantum state generation center devices. ∈ {1, 2,..., T}). The method for selecting the t quantum state generating center devices is not particularly limited, and any combination of quantum state generating center devices may be selected. Also, there is no particular limitation on the method of selecting P ₁ from the selected t number of quantum state generation center devices, and any quantum state generation center device may be designated as P ₁ .

As illustrated in FIG. 3, the quantum state generation center device 10-1 (P ₁ ) includes a random value generation unit 11-1, a secret value generation unit 12-1, a secret sharing unit 13-1, and a classical transmission unit 14. -1, classical reception unit 15-1, memory 16-1, complementary operation unit 17-1, quantum state generation unit 18-1, and quantum transmission unit 19-1, and classical transmission unit 14-1 and classical transmission unit 19-1. The receiving unit 15-1 is communicably connected to the classical communication path 30, and the quantum transmitting unit 19-1 is communicably connected to the quantum communication path 40.

<Structure of _{P s>}
FIG. 4 shows the quantum state generating center device 10-s (P _s ) other than P ₁ among the t quantum state generating center devices (P _r : rε {1, 2,..., T}). : Sε {2,..., T}) is a block diagram showing functions.
As illustrated in FIG. 4, the quantum state generation center device 10-s (P _s ) includes a random value generation unit 11-s, a secret value generation unit 12-s, a secret distribution unit 13-s, and a classical transmission unit 14. -S, classical reception unit 15-s, memory 16-s, complementary operation unit 17-s, quantum transmission unit 19-s, quantum reception unit 20-s and unitary transformation unit 21-s, classical transmission The unit 14-s and the classical receiver 15-s are communicably connected to the classical communication path 30, and the quantum transmitter 19-s and the quantum receiver 20-s are communicably connected to the quantum communication path 40. Yes.

<Configuration of P ₁ '>
FIG. 5A is a block diagram illustrating functions of the quantum state generation center device 10-1 (P ₁ ′). In this example, one quantum state generation center device belonging to t quantum state generation center devices selected from all the quantum state generation center devices is replaced with a quantum state generation center device 10-1 ( P ₁ ′). The method for selecting the t quantum state generating center devices is not particularly limited, and is not necessarily limited to the “t quantum state generating center devices (P _r ) shown in the column of <P ₁ , P _s >. : Rε {1, 2,..., T}) ”. Further, there is no particular limitation on the method for selecting P ₁ ′ from the selected t number of quantum state generation center devices, and any quantum state generation center device may be designated as P ₁ ′.

As illustrated in (a) of FIG. 5, the quantum state generation center device 10-1 includes a complementary operation unit 17-1, a quantum transmission unit 19-1, a quantum reception unit 20-1, and a unitary conversion unit 21-1. The quantum transmission unit 19-1 and the quantum reception unit 20-1 are connected to the quantum communication path 40 so as to communicate with each other.
The quantum state generation center device 10-1 also includes a random value generation unit 11, a secret value generation unit 12, a secret sharing unit 13, a classic transmission unit 14, a classic reception unit 15, and a memory 16 as illustrated in FIG. However, these descriptions are omitted in FIG.

<Configuration of P _c '>
FIG. 5B is a block diagram illustrating the functions of the quantum state generation center device 10-c (P _c ′: cε {2,..., T−1}). In this example, t−2 quantum state generation center devices (not including P ₁ ′) belonging to “t quantum state generation center devices” shown in the column <P ₁ ′> are included. The quantum state generating center device 10-c (P _c ′). The method for selecting P _c ′ (cε {1, 2,..., T−1}) is not particularly limited.

As illustrated in FIG. 5B, the quantum state generation center device 10-c includes a complementary operation unit 17-c, a quantum transmission unit 19-c, a quantum reception unit 20-c, and a unitary conversion unit 21-c. The quantum transmission unit 19-c and the quantum reception unit 20-c are communicably connected to the quantum communication path 40.
Further, the quantum state generating center device 10-c also includes a random value generating unit 11, a secret value generating unit 12, a secret sharing unit 13, a classic transmitting unit 14, a classic receiving unit 15, and a memory 16 as shown in FIG. However, these descriptions are omitted in FIG.

<Configuration of P _t '>
FIG. 5C is a block diagram illustrating functions of the quantum state generation center device 10-t (P _t ′). Note that the quantum state generation center device 10-t (P _t ′) is the remaining one quantum state belonging to “t quantum state generation center devices” shown in the column <P ₁ ′>. This is a generation center device.
As illustrated in FIG. 5C, the quantum state generation center device 10-t includes a complementary calculation unit 17-t, a quantum reception unit 20-t, a unitary conversion unit 21-t, an observation unit 22-t, and The determination unit 23-t is included, and the quantum reception unit 20-t is communicably connected to the quantum communication path 40.
In addition, the quantum state generation center device 10-t includes a random value generation unit 11, a secret value generation unit 12, a secret sharing unit 13, a classic transmission unit 14, a classic reception unit 15, and a memory as illustrated in FIG. 16 are omitted in FIG. 5C.

[Hardware configuration]
Next, a hardware configuration for realizing each configuration of the present embodiment will be exemplified.
For example, the random value generation unit 11, the secret value generation unit 12, the secret sharing unit 13, the classic transmission unit 14, the classic reception unit 15, the memory 16, and the complementary calculation unit 17 are executed by causing a known computer to execute a predetermined program. Built.

In addition, when the polarization of the photon is a qubit, the quantum state generation unit 18 uses, for example, parametric down conversion (PDC) (for example, “PG Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, AV Sergienko , and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett., 75: 4337-4341, 1995. “PG Kwiat, E. Waks, AG White, I. Appelbaum , and PH Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A, 60: R773-R776, 1999. ”), and the polarization angle of the transmitted light by the control voltage -An electro-optic effect modulator that can control the phase (for example, a Faraday rotator, a modulator that uses the electro-optic effect of a crystal such as LiNbO ₃ ), (1/2, 1/4) wavelength plate, acoustic element, liquid crystal It is constructed with elements and the like. Moreover, when using a quantum dot as a qubit, the quantum state production | generation part 18 is constructed | assembled by the production | generation apparatus of a quantum dot, and the apparatus which operates an electric field and a magnetic field, for example.

Further, when the unitary conversion unit 21 uses the polarization of the photon as a qubit, for example, an electro-optic effect modulator that can control the polarization angle and phase of the passing light by a control voltage, (1/2, 1/4) It is constructed by wave plates, acoustic elements, liquid crystal elements, and the like. Moreover, when using a quantum dot as a qubit, the unitary conversion part 21 is constructed | assembled by the apparatus which operates an electric field or a magnetic field, for example.
The observation unit 22 is a device that combines, for example, a beam splitter, a phase shifter, and a photon detector (a detector that can be used in a photon counting region such as a photomultiplier tube, a streak camera, a photodiode, or an avalanche photodiode). Can be used.

〔processing〕
Next, a quantum state generation method in this embodiment will be described.
<Preparation phase>
FIG. 6 is a flowchart for explaining the preparation phase of the quantum state generation process of this embodiment.
In the preparation phase, each quantum state generation center device 10-j (P _j : jε {1, 2,..., N}) distributes secrets to all the quantum state generation center devices. This preparation phase is executed in all quantum state generation center devices 10-j (P _j ).

First, in the random value generation unit 11 (FIG. 2) of each quantum state generation center device 10 (10-j), random values a _{j, i} ε {0,1} and b _{j, i} ε {0,1} (I∈ {1, 2,..., M}, where m is a natural number). These random values may be values selected by the user of each quantum state generation center device 10 or values set based on random numbers.
The generated random values a _{j, i} ε {0,1} and b _{j, i} ε {0,1} are respectively sent to the secret value generation unit 12, and the secret value generation unit 12 sets the secret value σ _j = {(A _{j, 1} , b _{j, 1} ), (a _{j, 2} , b _{j, 2} ),..., (A _{j, m} , b _{j, m} )} are generated (step S1).

The secret value σ _j generated by the secret value generation unit 12 of each quantum state generation center device 10-j (P _j ) is sent to each secret distribution unit 13, and each secret distribution unit 13 is, for example, finite. On the field GF (2 ^N ) (where N = 2m), using the Shamir secret sharing method (see, for example, “Modern cryptography” by Tatsuaki Okamoto and Hiroji Yamamoto (published industrial books) pages 209-218). , N variance values S _{j, q} (qε {1, 2,..., N}) of the secret value σ _j are generated. Specifically, the secret sharing unit 13 of each quantum state generation center device 10-j (P _j ), for example, uses S _{j, q} = f _j (on a finite field GF (2 ^N ) (N = 2m). x variance values S _{j, q} and n different points x _{j, q} (q∈ {1, 2,..., n}) satisfying x _{j, q} ) and σ _j = f _j (0) Are calculated (step S2). Here, f _j (x) is a (t−1) degree polynomial in which the secret is held in each quantum state generation center device 10-j (P _j ). Therefore, those who do not know this _f j (x), t sets of _{(S j, q, x j} , q) to acquire data can identify the first _{f j (x), σ j} = f j ( 0).

The points x _{j, q} generated by the secret sharing unit 13 of each quantum state generation center device 10-j (P _j ) are sent to the classical transmission unit 14, and from there for each quantum state generation through the classical communication path 30. It is transmitted to the center apparatus 10-q ( _Pq : qε {1, 2,..., N}) (step S3). In the case of this example, all the points x _{j and q} are open to all the quantum state generating center devices.
In addition, the distributed values S _{j, q} generated by the secret sharing unit 13 of each quantum state generating center device 10-j (P _j ) are sent to the classical communication unit 14, and from there through the classical communication path 30, the others _Is secretly transmitted to the center device _Pq for quantum state generation (step S4). The dispersion values S _{j, q} are transmitted one by one from each quantum state generation center device 10-j (P _j ) to each quantum state generation center device 10-q (P _q ). . Further, this secret transmission may be realized by a physically secure communication path or may be realized by an encryption technique. Further, the distributed value S _{j, j} generated by the secret sharing unit 13 of each quantum state generating center device 10-j (P _j ) is stored in the memory 16.

Then, the classical reception unit 15 of each quantum state generation center device 10-j (P _j ) receives the points x _{q, j} transmitted from the other quantum state generation center devices and stores them in the memory 16. (Step S5). Further, the classical reception unit 15 of each quantum state generation center device 10-j (P _j ) receives the distributed value S _{q, j} transmitted from the other quantum state generation center devices, and stores it in the memory 16. Store (step S6).

<Issuance phase>
FIG. 7 is a flowchart for explaining an issue phase of the quantum state generation processing of the present embodiment. Here, (a) shows the processing of the quantum state generation center device 10-1 (P ₁ ), and (b) shows the quantum state generation center device 10-s (P _s : sε {2, ..., t}).

In the issue phase, each of t (2 ≦ t ≦ n) quantum state generation center devices 10-r (P _r : rε {1, 2,..., T) selected from all the quantum state generation center devices. }) Cooperate to generate a quantum state | φ> corresponding to the entire secret information K. In this example, a protocol for continuously performing processing from the quantum state generation center device 10-1 (P ₁ ) to the quantum state generation center device 10-1 (P _t ) is shown, but the order is not important. There may be any order. That is, r of each quantum state generation center device 10-r (P _r ) is merely a symbol indicating the order of each quantum state generation center device that performs each process.

を満たす補完値
Ｋ^［ｒ］＝｛（ａ_１ ^［ｒ］，ｂ_１ ^［ｒ］），（ａ_２ ^［ｒ］，ｂ_２ ^［ｒ］），…，（ａ_ｍ ^［ｒ］，ｂ_ｍ ^［ｒ］）｝（ａ_ｉ ^［ｒ］∈｛０，１｝、ｂ_ｉ ^［ｒ］∈｛０，１｝、ｉ∈｛１，２，…，ｍ｝） …(1)
を、それぞれ算出する。 After the t number of quantum state generation center devices 10-r (P _r ) to cooperate, the t number of quantum state generation center devices 10-r (P _r : rε {1, 2,..., T }) Complementary operation units 17-1, 17-s (FIG. 3 and FIG. 4: sε {2,..., T}) are distributed values S _{q, r} stored in the memories 16-1, 16-s. From the exclusive OR

Complementary value ^K which satisfies the _{^{[r] = {(a 1}} [r], b 1 [r]), (a 2 [r], b 2 [r]), ..., (a m [r], b m [ ^r] )} (a _i ^[r] ∈ {0, 1}, b _i ^[r] ∈ {0, 1}, _i ∈ {1, 2,..., m}) (1)
Are calculated respectively.

Ｋ_ｒを求め（Ｋ_ｒはＧＦ（２^Ｎ）上）、その２進数表現を補完値Ｋ^［ｒ］とする（ステップＳ１１，Ｓ１５）。 Here, of course, each quantum state generation center device 10-r (P _r ) does not know the entire secret information K, and also knows the secret values σ _{q of} the other quantum state generation center devices 10-q (P _q ). Absent. The complementary operation units 17-1 and 17-s of the quantum state generation center device 10-r (P _r ) in this example include the variance values S _{q, r} , S _{r, r,} and the like from the memories 16-1 and 16 -s. Extract the point x _{q, r} (rε {1,2, ..., t}) and use the Lagrange complement formula,

_Kr is obtained ( _Kr is on GF ( ^2N )), and the binary representation is used as a complementary value K ^[r] (steps S11 and S15).

Then, the complementary value K ^[1] generated in the complementary calculation unit 17-1 of the quantum state generation center device 10-1 (P ₁ ) is sent to the quantum state generation unit 18-1 (FIG. 3), and the quantum state generator for the center device _{10-s (P} s) complementary value ^K generated by the complement arithmetic unit 17-s of ^[s] is sent to the quantum state generator 18-s (Fig. 4).

を生成する（ステップＳ１２）。 Next, in the quantum state generation unit 18-1 (FIG. 3) of the quantum state generation center device 10-1 (P ₁ ), the quantum state corresponding to the complementary value K ^[1].

Is generated (step S12).

は、Ｋ^［１］（ｒ＝１の場合における上述の式（１））において、ｂ_ｉ ^［１］＝０の場合にａ_ｉ ^［１］を第１の基底（｜ψ_０＞，｜ψ_１＞）で符号化し、ｂ_ｉ ^［１］＝１の場合にａ_ｉ ^［１］を第２の基底（α｜ψ_０＞＋β｜ψ_１＞，β^＊｜ψ_０＞‐α｜ψ_１＞（｜α｜^２＋｜β｜^２＝１、αは実数、βは複素数、β^＊はβの共役複素数））で符号化した量子状態を意味する。 Here, formula (2) is formed.

In K ^[1] (the above formula (1) when r = 1), when b _i ^[1] = 0, a _i ^{[1] is changed} to the first basis (| ψ ₀ >, | ψ ₁ >) and when b _i ^[1] = 1, a _i ^[1] is transformed into the second basis (α | ψ ₀ > + β | ψ ₁ >, β ^* | ψ ₀ > −α | ψ ₁ > (| Α | ² + | β | ² = 1, α is a real number, β is a complex number, and β ^* is a conjugate complex number of β)).

That is, the quantum state of Equation (3) is determined as follows.
| Ψ _0,0 > = | ψ ₀ >
| Ψ _1,0 > = | ψ ₁ >
| Ψ _0,1 > = α | ψ ₀ > + β | ψ ₁ >
| Ψ _1,1 > = β ^* | ψ ₀ > −α | ψ ₁ >
Specifically, for example, the first basis is (| 0>, | 1>), and the second basis is {(| 0> + | 1>) / √2, (| 0> − | 1>). ) / √2}
The quantum state of equation (3) is determined as follows.

| Ψ _0,0 > = | 0>
| Ψ _1,0 > = | 1>
| Ψ _0,1 > = (| 0> + | 1>) / √2
| Ψ _1,1 > = (| 0> − | 1>) / √2
The quantum state | φ ^[1] > generated by the quantum state generation unit 18-1 in this way is sent to the quantum transmission unit 19-1, and the quantum transmission unit 19-1 receives this quantum state | φ ^[1] >. Is transmitted to the center device 10-2 (P ₂ ) for quantum state generation (step S13).

Thereafter, the following processing is repeated in the order of quantum state generation center devices 10-2 (P ₂ ), 10-3 (P ₃ ),..., 10-t (P _t ). In the following, the symbol s (sε {2,..., T}) is used, and these processes are generalized and described.
First, the quantum reception unit 20-s (FIG. 4) of the quantum state generation center device 10-s (P _s : sε {2,..., T}) ) The quantum state | φ ^[s-1] > transmitted from (P _s-1 ) is received (step S16).

を施し、量子状態｜φ^［ｓ］＞を生成する（ステップＳ１７）。 The received quantum state | φ ^[s-1] > is sent to the unitary transform unit 21-s, and the unitary transform unit 21-s responds to this quantum state | φ ^[s-1] > in step S15. Unitary transformation corresponding to the complementary value K ^[s] (the above-described equation (1) in the case of r = s ⁾ sent from the complementary arithmetic unit 17-s

To generate a quantum state | φ ^[s] > (step S17).

が示すａ_ｉ ^{［ｓ-１］}へ符号化した量子状態への変換を行い、ａ_ｉ ^［ｓ］＝１の場合、式（５）の量子状態が示すａ_ｉ ^{［ｓ-１］}を反転させた量子状態への変換を行うユニタリ変換である。また、Ｖ_ｉ ^［ｓ］は、ｂ_ｉ ^［ｓ］＝０の場合、式（５）の量子状態の基底で符号化した量子状態への変換を行い、ｂ_ｉ ^［ｓ］＝１の場合、式（５）の量子状態の基底とは異なる基底で符号化した量子状態への変換を行うユニタリ変換である。 Note that U _i ^[s] (i∈ {1, 2,..., M}) in Expression (4) is received when the element of the complementary value K ^[s] is a _i ^[s] = 0. Quantum state which is an element of quantum state | φ ^[s-1] >

Is converted to a quantum state encoded to a _i ^[s-1] , and when a _i ^[s] = 1, a _i ^[s-1] indicated by the quantum state of Expression (5) is inverted. It is a unitary transformation that transforms into a quantum state. V _i ^[s] is converted into a quantum state encoded by the base of the quantum state of Equation (5) when b _i ^[s] = 0, and when b _i ^[s] = 1, It is a unitary transformation that performs transformation to a quantum state encoded with a basis different from the basis of the quantum state of Equation (5).

であり、Ｖ_ｉ ^［ｓ］は、

である（ここで、ユニタリ変換Ｕ_ｉ ^［ｓ］，Ｖ_ｉ ^［ｓ］の基底は上記第１の基底（｜ψ_０＞，｜ψ_１＞）である。）。 Specifically, the first basis is (| ψ ₀ >, | ψ ₁ >), and the second basis is (α | ψ ₀ > + β | ψ ₁ >, β ^* | ψ ₀ > −α | ψ ₁ > (| α | ² + | β | ² = 1, α is a real number, β is a complex number)), U _i ^[s] is

And V _i ^[s] is

(Here, the bases of the unitary transformations U _i ^[s] and V _i ^[s] are the first bases (| ψ ₀ >, | ψ ₁ >)).

であり、Ｖ_ｉ ^［ｓ］は、

である（ここで、Ｈはアダマール（Ｈａｄａｍａｒｄ）変換であり、ユニタリ変換Ｕ_ｉ ^［ｓ］，Ｖ_ｉ ^［ｓ］の基底は上記第１の基底（｜０＞，｜１＞）である。）。 More specifically, for example, the first base is (| 0>, | 1>) and the second base is {(| 0> + | 1>) / √2, (| 0> − | 1>) / √2}, U _i ^[s] is

And V _i ^[s] is

(Here, H is a Hadamard transform, and the bases of the unitary transforms U _i ^[s] and V _i ^[s] are the first bases (| 0>, | 1>).) .

の関係が成り立つ量子状態｜ψ’＞＝ｃ_３｜ψ_０＞＋ｃ_４｜ψ_１＞に変換することを意味する。 “Applying unitary transformation U to quantum state | ψ>” means that quantum state | ψ> = c ₁ | ψ ₀ > + c ₂ | ψ ₁ > (where | ψ ₀ >, | ψ ₁ > First base)

That is, the quantum state | ψ ′> = c ₃ | ψ ₀ > + c ₄ | ψ ₁ > is satisfied.

The quantum state | φ ^[s] > generated as described above is sent to the quantum transmitter 19-1, from which the quantum state generating center device 10- (s + 1) (P _{s + 1} ) is transmitted through the quantum communication path 40. (Step S18). When s = t, this quantum state | φ ^[s] > is transmitted to, for example, a quantum state generation center device that first executes the verification phase described below. (A) of FIG. 9 is a figure which showed transition of the quantum state in the above issue phase.

に対応する量子状態｜φ＞とする。なお、式（６）（７）におけるΣは、排他的論理和のΣ演算を意味する。 As shown in this Figure, the quantum state is generated in the quantum state generating center device P ^₁ | φ ^_[1]> is sent to the quantum state generating center device P _2. The quantum state generating center device P ₂ is this by performing unitary transformation described above quantum state | generate the phi ^[2]>, which is sent to the next quantum state generating center apparatus P _3. Then, the same processing is repeated up to the quantum state generation center device P _t , and the quantum state | φ ^[t] > output therefrom is changed to the whole secret information.

It is assumed that the quantum state | φ> corresponding to. In the equations (6) and (7), Σ means an exclusive OR Σ operation.

[Reason why quantum state | φ ^[t] > corresponds to global secret information K]
As described above, the unitary transformation W ^[s] is expressed by Expression (4), and U _i ^[s] (i∈ {1, 2,..., M}) in Expression (4) is the complementary value K ^{[s. elements]} _are, for ^{a i [s]} = 0, performs conversion to a quantum state of encoding to _a ^{i [s-1]} indicated by the quantum state of the formula ^{_{(5), a i [s}} ] = 1 Is a unitary transformation that performs transformation to a quantum state obtained by inverting a _i ^[s-1] indicated by the quantum state of Equation (5). V _i ^[s] is converted into a quantum state encoded by the base of the quantum state of Equation (5) when b _i ^[s] = 0, and when b _i ^[s] = 1, It is a unitary transformation that performs transformation to a quantum state encoded with a basis different from the basis of the quantum state of Equation (5).

の演算結果に対応する量子状態を生成することを意味する。そのため、上述のように量子状態生成用センター装置でユニタリ変換を順次繰り返していった結果は、式（７）に対応する量子状態となる。また、式（６）＝式（７）となるのは、シャミアの秘密分散法（例えば岡本龍明・山本博次著「現代暗号」（産業図書発行）Ｐ２０９〜２１８頁参照。）の性質から明らかである。 This is because these unitary transformations are exclusive ORs.

This means that a quantum state corresponding to the operation result of is generated. Therefore, as described above, the result of sequentially repeating unitary transformations in the quantum state generating center device is a quantum state corresponding to Equation (7). The formula (6) = formula (7) is based on the property of Shamir's secret sharing method (for example, see Tatsuaki Okamoto and Hiroji Yamamoto “Modern Crypto” (published industrial books) pages 209 to 218). it is obvious.

<Verification phase>
FIG. 8 is a flowchart for explaining the verification phase of this embodiment. Here, (a) shows the processing of the quantum state generation center device 10-c (P _c ′: cε {1, 2,..., T−1}), and (b) shows the quantum state generation processing. The process of center apparatus 10-t ( _Pt ') is shown.
In the verification phase, each of t (2 ≦ t ≦ n) quantum state generation center devices 10-c, 10-t (P ₁ ′,..., P _t ′) selected from all the quantum state generation center devices. ) Cooperate to verify the validity of the quantum state | φ> = | φ ^[0] '> generated in the issue phase. In this example, a protocol for continuously performing processing from the quantum state generation center device 10-1 (P ₁ ') to the quantum state generation center device 10-1 (P _t ') is shown. It is not important and can be in any order. Further, the quantum state generating center device participating in the verification phase may be the same as or different from the quantum state generating center device participating in the issuing phase. However, in order to prevent fraudulent collusion by the quantum state generation center device participating in the issue phase, it is desirable that the quantum state generation center device not participating in the issue phase participate in this verification phase.

を量子状態｜φ^［０］’＞に対して施し、量子状態｜φ^［１］’＞を生成する（ステップＳ２２）。生成された量子状態｜φ^［１］’＞は、量子送信部１９−１に送られ、そこから量子通信路４０を通じ、量子状態生成用センター装置１０−２（Ｐ_２’）に送信される（ステップＳ２３）。
その後、量子状態生成用センター装置１０−２（Ｐ_２’），１０−３（Ｐ_３），…，１０−（ｔ−１）（Ｐ_ｔ−１）という順番で以下の処理が繰り返される。以下では、記号ｃ（ｃ∈｛２，…，ｔ‐１｝）を用い、これらの処理を一般化して記載する。 First, the quantum reception unit 20-1 (FIG. 5A) of the quantum state generation center device P ₁ ′ receives the quantum state | φ ^[0] ′> to be verified (step S21) and converts it to unitary transformation. Send to part 21-1. The unitary conversion unit 21-1 performs unitary conversion corresponding to the complementary value K ^[1] sent from the complementary calculation unit 17-1, similarly to step S17.

Is applied to the quantum state | φ ^{[0 ]} '> to generate the quantum state | φ ^[1] '> (step S22). The generated quantum state | φ ^[1] ′> is sent to the quantum transmitter 19-1, from which it is transmitted to the quantum state generation center device 10-2 (P ₂ ′) through the quantum communication path 40. (Step S23).
Thereafter, the following processes are repeated in the order of quantum state generation center devices 10-2 (P ₂ ′), 10-3 (P ₃ ),..., 10- (t−1) (P _t−1 ). In the following, these processes are generalized and described using the symbol c (cε {2,..., T−1}).

を施し、量子状態｜φ^［ｃ］’＞を生成する（ステップＳ２２）。生成された量子状態｜φ^［ｃ］’＞は量子送信部１９−ｃに送られ、量子送信部１９−ｃは、この量子状態｜φ^［ｃ］’＞を、量子状態生成用センター装置１０−（ｃ＋１）（Ｐ_ｃ＋１’）に送信する（ステップＳ２３）。 First, it is transmitted from the 'quantum receiving unit 20-c in (Fig. 5 (b)), the quantum state generating center apparatus _{10- (c-1) (P} c-1' quantum state generating center apparatus _{P c)} Quantum state | φ ^[c-1] ′> is received (step S21), and is sent to the unitary conversion unit 21-c. The unitary conversion unit 21-c applies a unitary conversion corresponding to the complementary value K ^[c] sent from the complementary operation unit 17-c to the quantum state | φ ^[c-1] '> in the same manner as in step S17.

To generate a quantum state | φ ^[c] ′> (step S22). The generated quantum state | φ ^[c] ′> is sent to the quantum transmitter 19-c, and the quantum transmitter 19-c converts the quantum state | φ ^[c] ′> into the quantum state generation center device 10. -(C + 1) ( _{Pc + 1} ') is transmitted (step S23).

を施し、量子状態｜φ^［ｔ］’＞を生成する（ステップＳ２６）。 The above process is repeated up to the quantum state generation center device 10- (t-1) ( _Pt-1 '), and the quantum state transmitted from the quantum state generation center device _Pt-1 ' | φ ^{[t-1 ]} Is received by the quantum receiving unit 20-t of the quantum state generating center device 10-t ( _Pt ') (step S25) and sent to the unitary conversion unit 21-t. The unitary conversion unit 21-t applies a unitary conversion corresponding to the complementary value K ^[t] sent from the complementary operation unit 17-t to the quantum state | φ ^[t-1] '> as in step S17.

To generate a quantum state | φ ^[t] ′> (step S26).

The generated quantum state | φ ^[t] ′> is sent to the observation unit 22-t, where it is observed by the basis (0,..., 0) (all are the first basis) (step S27). The binary sequence (a ₁ ′, a ₂ ′,..., A _m ′), which is the observation result, is sent to the determination unit 23-t, which determines the binary sequence (a ₁ ′, a ₂ ′,..., A _m ′), it is determined whether or not all elements a _i ′ (iε {1,..., M}) are 0 (step S28). Here, when any element a _i ′ of this binary number sequence (a ₁ ′, a ₂ ′,..., A _m ′) is not 0, the determination unit 23-t determines the quantum state | It is determined that φ ^[0] ′> is invalid (step S30). On the other hand, if all elements a _i ′ are 0, it is determined that the quantum state | φ ^[0] ′> to be verified is valid.

FIG. 9B is a diagram showing the transition of the quantum state in the above verification phase.
As shown in this figure, _'quantum states to be verified to | phi ^[0]' quantum state generating center device P ₁ to enter>, quantum state by performing unitary transformation in the quantum state generating center device P _{1 '} | Φ ^[1] '> is generated. The generated quantum state | φ ^[1] '> is sent to the quantum state generation center device P ₂ , and then the same processing is repeated up to the quantum state generation center device P _t−1 , and the last quantum state generation center The unit Pt is subjected to a unitary transformation on the quantum state | φ ^[t−1] '> in the device P _t , the resulting quantum state | φ ^[t] '> is observed, and the quantum state to be verified | φ ^[0] ' Judge the validity of>.

[Reason why it can be said that the elements a _i 'of the observation result are all zero]
In published phase (FIG. 9 (a)), the quantum state is generated corresponding to the complementary value K ^[1] in a quantum state generating center device P _{1, t-1} one quantum state generating center apparatus P _s Oite , The unitary transformation corresponding to the complementary value K ^[s] is performed, and the quantum state corresponding to the entire secret information K is generated. Here, generating a quantum state corresponding to the complementary value ^{K [1], (0,} ..., 0) is subjected to unitary transformation corresponding to the complementary value K ^[1] to the quantum state corresponding to the same meaning It is.

In the verification phase (FIG. 9B), unitary transformations corresponding to the complementary values K ^[c] are performed in the t quantum state generation center devices P _c ′, respectively.
As described above, the operation result as the entire issue phase is equal to the operation result as the entire verification phase. As described above, in this embodiment, each unitary transformation corresponds to an exclusive OR operation, so performing the issue phase and the verification phase corresponds to taking the exclusive OR of the same values. . Therefore, if the issue phase is valid, the observation result of the output value in the verification phase should be (0,..., 0). Thereby, the validity of the quantum state generated in the issue phase can be verified.

  The present invention is not limited to the embodiment described above. For example, all the quantum state generating center devices may have all the configurations shown in FIGS. The various processes described above are not only executed in time series according to the description, but may also be executed in parallel or individually as required by the processing capability of the apparatus that executes the processes. Needless to say, other modifications are possible without departing from the spirit of the present invention. When realizing a function for handling classical information such as a random value generating unit 11, a secret value generating unit 12, a secret sharing unit 13, a classical transmitting unit 14, a classical receiving unit 15, a memory 16 and a complementary calculating unit 17 by a classical computer, The processing content of the function is described by a program. The processing functions are realized on the computer by executing the program on the computer.

  Further, when the control of the functions that handle quantum information such as the quantum state generation unit 18 and the unitary conversion unit 21 is realized by a classical computer, the processing content of the control function is described by a program. The program in this case means, for example, a program for causing a computer to control the frequency and time of the electromagnetic wave applied to the nuclear spin when the nuclear spin is used for the qubit, and the photon is used for the qubit. When used, it means a program for causing a computer to control the characteristics of each optical element necessary for quantum processing (for example, mirror angle, phase shifter control voltage, etc.). The control function is realized on the computer by executing the program on the computer.

  The program describing these processing contents can be recorded in a computer-readable recording medium. The computer-readable recording medium may be any medium such as a magnetic recording device, an optical disk, a magneto-optical recording medium, or a semiconductor memory. Specifically, for example, the magnetic recording device may be a hard disk device or a flexible Discs, magnetic tapes, etc. as optical disks, DVD (Digital Versatile Disc), DVD-RAM (Random Access Memory), CD-ROM (Compact Disc Read Only Memory), CD-R (Recordable) / RW (ReWritable), etc. As the magneto-optical recording medium, MO (Magneto-Optical disc) or the like can be used, and as the semiconductor memory, EEP-ROM (Electronically Erasable and Programmable-Read Only Memory) or the like can be used.

  The program is distributed by selling, transferring, or lending a portable recording medium such as a DVD or CD-ROM in which the program is recorded. Furthermore, the program may be distributed by storing the program in a storage device of the server computer and transferring the program from the server computer to another computer via a network.

A computer that executes such a program first stores, for example, a program recorded on a portable recording medium or a program transferred from a server computer in its own storage device. When executing the process, the computer reads the program stored in its own recording medium and executes the process according to the read program. As another execution form of the program, the computer may directly read the program from a portable recording medium and execute processing according to the program, and the program is transferred from the server computer to the computer. Each time, the processing according to the received program may be executed sequentially. Also, the program is not transferred from the server computer to the computer, and the above-described processing is executed by a so-called ASP (Application Service Provider) type service that realizes the processing function only by the execution instruction and result acquisition. It is good. Note that the program in this embodiment includes information that is used for processing by an electronic computer and that conforms to the program (data that is not a direct command to the computer but has a property that defines the processing of the computer).
In this embodiment, the present apparatus is configured by executing a predetermined program on a computer. However, at least a part of these processing contents may be realized by hardware.

  As an industrial application field of the present invention, distributed cipher (threshold cipher) in quantum communication can be exemplified. Specifically, the present invention can be applied to, for example, quantum cash, quantum voting, quantum bidding, and the like.

The figure which showed the whole structure of the quantum state production | generation system of this form. The block diagram which showed the function structure which all the center apparatuses for quantum state production | generation have in common. The block diagram which showed the function structure which the center apparatus for quantum state generation regarding an issue phase has in common. The block diagram which showed the function structure which the center apparatus for quantum state generation regarding an issue phase has in common. The block diagram which showed the function structure which the center apparatus for quantum state generation in connection with a verification phase has in common. The flowchart for demonstrating the preparation phase of the quantum state production | generation process of this form. The flowchart for demonstrating the issue phase of the quantum state production | generation process of this form. The flowchart for demonstrating the verification phase of this form. (A) is the figure which showed transition of the quantum state in the above issue phase. (B) is a diagram showing the transition of the quantum state in the verification phase described above.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Quantum state generation system 10 Center apparatus for quantum state generation

Claims (10)

A quantum state generation method executed by n (n ≧ 2) quantum state generation center devices,
The secret value generating unit of each quantum state generating center device P _j (j∈ {1, 2,..., N}) performs the respective secret values σ _j = {(a _{j, 1} , b _{j, 1} ), ( _{aj, 2} , bj _{, 2} ), ..., ( _{aj, m} , bj _{, m} )} ( _{aj, i [} epsilon] {0,1}, bj _{, i [} epsilon] {0,1}, _i [epsilon] {1, 2,..., M}, where m is a natural number)
A distributed value generating step in which the secret sharing unit of each quantum state generating center device P _j generates a distributed value S _{j, q} (qε {1, 2,..., N}) of the secret value σ _j ;
A distributed value transmission step in which the classical transmission unit of each quantum state generation center device P _j secretly transmits the dispersion values S _{j, q} to the quantum state generation center device P _q ;
A dispersion value receiving step in which the classical reception unit of each quantum state generation center device P _j receives the dispersion values S _{q, j} transmitted from the other quantum state generation center devices P _q ;
The complementary operation units of the t (2 ≦ t ≦ n) quantum state generation center devices P _r (rε {1, 2,..., t}) do not know the entire secret information K, and the variance value S _{From q and r} , exclusive OR

Complementary value ^K which satisfies the _{^{[r] = {(a 1}} [r], b 1 [r]), (a 2 [r], b 2 [r]), ..., (a m [r], b m [ ^r] )} (a _i ^[r] ∈ {0, 1}, b _i ^[r] ∈ {0, 1}, _i ∈ {1, 2,..., m}) respectively. When,
The quantum state generation unit of the quantum state generation center device P ₁

A quantum state generation step for generating
A first quantum state transmitting step in which a quantum transmitter of the quantum state generating center device P ₁ transmits the quantum state | φ ^[1] > to the quantum state generating center device P ₂ ;
The quantum receiving unit of the quantum state generating center device P _s (sε {2,..., T}) receives the quantum state | φ ^[s-1] > transmitted from the quantum state generating center device P _s-1. Receiving a quantum state receiving step;
The unitary transformation unit of the quantum state generation center device P _s performs unitary transformation on the quantum state | φ ^[s-1] >.

A unitary conversion step,
The quantum state | φ ^[s-1]> the quantum state is a result of applying the unitary transformation W ^[s] | a φ ^[s]>, quantum transmitter portion of the quantum state generating center apparatus P _s to send A second quantum state transmission step;
A quantum state generation method characterized by comprising: The quantum state generation method according to claim 1,
The variance value generation step includes
On the finite field GF (2 ^N ) (N = 2m), S _{j, q} = f _j (x _{j, q} ) and σ _j = f _j (0) (f _j (x) is a (t−1) degree polynomial. ) Satisfying the equation, n dispersion values S _{j, q} and n different points x _{j, q} (qε {1, 2,..., N}) are represented by each quantum state generating center device P _j . A step of calculating by the secret sharing unit,
The distributed value transmission step includes
The classical transmission unit of each quantum state generation center device P _j further transmits the n different points x _{j, q} to each quantum state generation center device,
The distributed value receiving step includes
The classical reception unit of each quantum state generation center device P _j receives n different points x _{q, j} transmitted from the other quantum state generation center devices P _q ,
In the complementary value calculation step, the complementary calculation units of the t quantum state generating center devices _Pr include

Is a step of calculating a binary representation of as a complementary value K ^[r] .
A quantum state generation method characterized by the above. The quantum state generation method according to claim 1 or 2,
The first basis is
(| Ψ ₀ >, | ψ ₁ >)
And
The second basis is
(Α | ψ ₀ > + β | ψ ₁ >, β ^* | ψ ₀ > -α | ψ ₁ >)
(| Α | ² + | β | ² = 1, α is a real number, β is a complex number, β ^* is a conjugate complex number of β)
And
_U ^{i [s]} is the unitary transformation ^{W [s],}

And
V _i ^[s] is

(Here, the bases of the unitary transformations U _i ^[s] and V _i ^[s] are the first bases (| ψ ₀ >, | ψ ₁ >)).
A quantum state generation method characterized by the above. The quantum state generation method according to claim 1 or 2,
The first basis is
(| 0>, | 1>)
And
The second basis is
{(| 0> + | 1>) / √2, (| 0> − | 1>) / √2}
And
_U ^{i [s]} is the unitary transformation ^{W [s],}

And
V _i ^[s] is

(Here, the bases of the unitary transformations U _i ^[s] and V _i ^[s] are the first bases (| 0>, | 1>)).
A quantum state generation method characterized by the above. A quantum state generation method according to any one of claims 1 to 4,
The unitary transformation unit of the quantum state generation center device P ₁ ′ performs unitary transformation on the quantum state | φ ^[0] ′> to be verified.

Applying steps,
Quantum state that is the result of applying the unitary transformation W ^[1] to the quantum state | φ ^[0] '>
φ ^[1] '> is transmitted from the quantum transmitter of the quantum state generating center device P ₁ ′ to the quantum state generating center device P ₂ ′;
Quantum state generating center apparatus _{P c '(c∈ {2,} ..., t-1}) unitary transformation unit of the quantum state generating center apparatus _{P c-1'} quantum state transmitted from | phi ^{[c- 1]} Unit conversion for '>

Applying steps,
The quantum state ^{| φ [c-1] '} > to the unitary transformation W quantum state is a result of applying the ^{[c] | φ [c]} 'a>, quantum transmitting unit of the quantum state generating center apparatus P _{c '} Transmitting to the quantum state generating center device P _{c + 1} ′,
The unitary transformation unit of the quantum state generation center device P _t ′ performs unitary transformation on the quantum state | φ ^[t−1] ′> transmitted from the quantum state generation center device P _t-1 ′.

Applying steps,
The result of unitary transformation W ^[t] applied to the quantum state | φ ^[t-1] '> is obtained from the observation unit of the quantum state generation center device P _t ' using the basis (0, ..., 0) (all first Observing at the base of
When any element a _i ′ of the binary sequence (a ₁ ′, a ₂ ′,..., A _m ′) which is an observation result in the observation unit of the quantum state generating center device P _t ′ is not 0 The determination unit determines that the quantum state | φ ^[0] '> to be verified is invalid;
A quantum state generation method comprising: Secret value σ ₁ = {(a _1,1 , b _1,1 ), (a _1,2 , b _1,2 ), ..., (a _{1, m} , b _{1, m} )} (a _{1, i} ∈ {0, 1}, b _{1, i} ∈ {0, 1} _{, i} ∈ {1, 2,..., M}, where m is a natural number)
A secret sharing unit that generates a distributed value S _{1, q} (qε {1, 2,..., N}) of the secret value σ ₁ ;
A classical transmission unit that secretly transmits the dispersion value S1 _{, q} to another quantum state generation center device _Pq ;
A classical reception unit that receives the dispersion value S _{q, 1} transmitted from another quantum state generating center device P _q ;
From the variance S _{q, 1} , the exclusive OR

Complementary value ^{K _[1]} = satisfying _{^{{(a 1 [1],}} b 1 [1]), (a 2 [1], b 2 [1]), ..., (a m [1], b m [ ^1] )} (a _i ^[1] ∈ {0, 1}, b _i ^[1] ∈ {0, 1}, _i ∈ {1, 2,..., M});
Quantum state

A quantum state generator for generating
A quantum transmitter that transmits the quantum state | φ ^[1] > to the quantum state generating center device P ₂ ;
A quantum state generating center device characterized by comprising: Secret value σ _s = {(a _{s, 1} , b _{s, 1} ), (a _{s, 2} , b _{s, 2} ), ..., (a _{s, m} , b _{s, m} )} (a _{s, i} ∈ {0,1}, b _{s, i} ∈ {0,1}, i∈ {1, 2,..., M}, s∈ {2,..., T}, 2 ≦ t ≦ n, n is 2 or more A secret value generator that generates a natural number, m is a natural number),
A secret sharing unit that generates a distributed value S _{s, q} (qε {1, 2,..., N}) of the secret value σ _s ;
A classical transmission unit that secretly transmits the dispersion value S _{s, q} to another quantum state generation center device P _q ;
A classical receiver that receives the dispersion values S _{q, s} transmitted from the other quantum state generating center device P _q ;
Without knowing the total secret information K from the variance values S _{q, s} , exclusive OR

Satisfying complementary values K ^[s] = {(a ₁ ^[s] , b ₁ ^[s] ), (a ₂ ^[s] , b ₂ ^[s] ),..., (A _m ^[s] , b _m ^[S] )} (a _i ^[s] ∈ {0, 1}, b _i ^[s] ∈ {0,
1}, i∈ {1, 2,..., M}),
Quantum state transmitted from center device P _s-1 for quantum state generation

A quantum receiver for receiving
Unitary transformation for the quantum state | φ ^[s-1] >

A unitary converter for applying
A quantum transmitter that transmits a quantum state | φ ^[s] > that is a calculation result in the unitary converter;
A quantum state generating center device characterized by comprising: The quantum state generating center device according to claim 6 or 7,
The above complement calculation unit
On a finite field GF (2 ^N ) (N = 2m), S _{r, q} = f _r (x _{r, q} ) and σ _r = f _r (0) (f _r (x) is a (t−1) degree polynomial. ) And n variance values S _{r, q} and n different points x _{r, q} (qε {1, 2,..., N}) satisfying
The classical transmitter is
Further, the n different points x _{r, q} are transmitted to each quantum state generating center device,
The classical receiver is
Furthermore, n different points x _{q, r} transmitted from other quantum state generating center device P _q are received,
The above complement calculation unit

Is calculated as a complementary value K ^[r] .
A quantum state generating center device. The center device for quantum state generation according to claim 7,
The first basis is
(| Ψ ₀ >, | ψ ₁ >)
And
The second basis is
(Α | ψ ₀ > + β | ψ ₁ >, β ^* | ψ ₀ > -α | ψ ₁ >)
(| Α | ² + | β | ² = 1, α is a real number, β is a complex number, β ^* is a conjugate complex number of β)
And
_U ^{i [s]} is the unitary transformation ^{W [s],}

And
V _i ^[s] is

(Here, the bases of the unitary transformations U _i ^[s] and V _i ^[s] are the first bases (| ψ ₀ >, | ψ ₁ >)).
A quantum state generating center device. The center device for quantum state generation according to claim 7,
The first basis is
(| 0>, | 1>)
And
The second basis is
{(| 0> + | 1>) / √2, (| 0> − | 1>) / √2}
And
_U ^{i [s]} is the unitary transformation ^{W [s],}

And
V _i ^[s] is

(Here, the bases of the unitary transformations U _i ^[s] and V _i ^[s] are the first bases (| 0>, | 1>)).
A quantum state generating center device.

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