KR102108892B1 - Method of identifying bell type state - Google Patents

Abstract

According to the present invention, a quantum bell state identification method includes the steps of: performing the polarization of a photon, by a first device, and then providing the same to each of a plurality of paths; generating, by the first device, a message indicating a path of the photon according to whether a photon exists in each of the plurality of paths, and providing the message to the second device; applying, by the second device, a predetermined operator based on the message to an electron; and estimating the initial state of the photon by applying, to the electron, an operator corresponding to the polarization state of the photon among a plurality of operators based on the message by the second device according to the bell type state of the photon.

Description

Quantum Bell Status Identification Method {METHOD OF IDENTIFYING BELL TYPE STATE}

The present invention relates to a quantum bell state identification method, and more particularly, to a quantum bell state identification method that enables the identification of a bell type state without particle exchange using reflection performance communication between two devices.

The basic unit of information is a qubit, not a bit, and a qubit means all possible quantum overlapping states of 0 and 1, not two distinct physical states represented by 0 and 1.

That is, only 0 or 1 can be expressed in the case of bits, but in the case of qubit, 0 and 1 can be simultaneously expressed due to the principle of quantum overlapping, and thus can be implemented only using a quantum mechanical physics system with quantum coherence.

One of the most bizarre features of quantum mechanics, quantum entanglement, is a phenomenon that occurs even when the correlations appearing in quantum systems are space-time distant, that is, non-local characteristics.

The most representative and basic form of bilateral entanglement is the bell state. At this time, in order to distinguish quantum entanglement, the bell state must be measured, but there is a problem that the bell state cannot be accurately identified.

An object of the present invention is to provide a quantum bell state identification method that enables identification of a bell type state without particle exchange using reflection performance communication between two devices.

The objects of the present invention are not limited to the above-mentioned objects, and other objects and advantages of the present invention not mentioned can be understood by the following description, and will be more clearly understood by embodiments of the present invention. In addition, it will be readily appreciated that the objects and advantages of the present invention can be realized by means of the appended claims and combinations thereof.

The quantum bell state identification method for achieving the above object comprises the steps of providing a plurality of paths to a plurality of paths after the first device performs polarization of photons, and the first device to determine whether photons exist in each of the plurality of paths. Generating a message indicating a path of a photon and providing it to a second device, applying a predetermined operator to the former based on the message by the second device, and allowing the second device to set the photon's bell type state Accordingly, based on the message, applying an operator corresponding to the polarization state of the photon among the plurality of operators to the electron to estimate the initial state of the photon.

According to the present invention as described above, there is an advantage in that the bell-type state can be identified without particle exchange by using reflective performance communication between two devices.

1 is a view for explaining a conventional quantum network system.
2 is a view for explaining a quantum bell type identification system according to an embodiment of the present invention.
3 is a view for explaining the internal structure of the first device of FIG. 2.
4 is a flowchart for explaining an embodiment of a method for identifying a quantum bell state according to the present invention.

The above-described objects, features, and advantages will be described in detail below with reference to the accompanying drawings, and accordingly, a person skilled in the art to which the present invention pertains can easily implement the technical spirit of the present invention. In the description of the present invention, when it is determined that detailed descriptions of known technologies related to the present invention may unnecessarily obscure the subject matter of the present invention, detailed descriptions will be omitted. Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. The same reference numerals in the drawings are used to indicate the same or similar components.

1 is a view for explaining a conventional quantum network system.

(140) 및 V(H)-QZ 게이트(150)를 포함한다. Referring to FIG. 1, the first device 100 includes an optical circulator 110, an H (V) -QZ gate 120, a switch mirror 130,

140 and V (H) -QZ gate 150.

The photon in the H (V) state is input to the H (V) -QZ gate 120 through the light circulator 110, and the H (V) -QZ gate 120 is in the H (V) state while being executed M times Converts photons of and outputs photons.

(140)에 제공되거나

(140)에 제공되지 않는다. 즉, 광자는 스위치 미러(130)의 상태가 오프 상태이면 광자를 수신하여

(140)에 제공되지만, 스위치 미러(130)의 상태가 온 상태이면 반사되어

(140)에 제공되지 않는다.The photon passing through the H (V) -QZ gate 120 depends on the state of the switch mirror 130

Provided at 140 or

It is not provided at 140. That is, when the state of the switch mirror 130 is off, the photon receives the photon

It is provided to 140, but is reflected when the state of the switch mirror 130 is on

It is not provided at 140.

(140)에 제공하기 위해 오프 상태를 유지하며 광자가

(140)에 제공된 후에 오프 상태에서 온 상태로 변경하여 다음에 수신되는 광자를 반사시켜

(140)에 제공되지 않도록 한다. To this end, the initial state of the switch mirror 130 allows photons to pass through

Keeps it off to provide to 140 and photons

After being provided to 140, change from off to on to reflect the next photon received

(140).

(140)에 제공되지 않으며, 특정 횟수(예를 들어, 3번)의 광자를 반사시킨 후에는 오프 상태에서 온 상태로 변경되어 다음에 수신된 광자를 통과시켜

(140)에 제공한다.As described above, since the state of the switch mirror 130 remains off, the next photon received is reflected.

It is not provided in (140), and after reflecting a specific number of photons (for example, 3 times), it is changed from the off state to the on state and then passed through the received photon

(140).

(140)는 광자의 상태에 따라 광자를 통과시켜 V(H)-QZ 게이트(150)에 제공하거나 제공하지 않는다. 즉,

(140)는 광자의 상태가 V(H)인 경우 광자를 통과시켜 V(H)-QZ 게이트(150)에 제공하고, 광자의 상태가 H(V)인 경우 광자를 통과시키지 않고 반사시켜 광자가 V(H)를 V(H)-QZ 게이트(150)에 제공되지 않도록 한다. V(H)-QZ 게이트(150)는 N번 실행되는 동안 V(H) 상태의 광자를 변환시켜 광자를 출력하여 제2 장치(200)에 제공한다.

Depending on the state of the photon, 140 passes through the photon and provides or does not provide it to the V (H) -QZ gate 150. In other words,

When the photon state is V (H), the photon passes through the photon and is provided to the V (H) -QZ gate 150. When the photon state is H (V), the photon is reflected without passing through the photon. Let V (H) not be provided to V (H) -QZ gate 150. The V (H) -QZ gate 150 converts the photon in the V (H) state during N times of execution and outputs the photon and provides it to the second device 200.

2 is a view for explaining a quantum bell type identification system according to an embodiment of the present invention.

Referring to FIG. 2, the quantum bell type identification system includes a first device 100 and a second device 200. The first device 100 and the second device 200 share a bell type photon and electron pair. At this time, electrons are used as quantum absorbent objects.

There are four types of orthogonal bell-type states, as shown in [Equation 2] to [Equation 5] below.

(.) *: | pass> e = | 0> e = | 0> L | 1> U, | block> e = | 1> e = | 1> L | 0> U, | H> p = | 0 complex of> p and | V> p = | 1> p,

e: electronic,

P: photon,

L, U: electron path

The variables a, b, c, and d follow conditions such as [Equation 6] and [Equation 7] below.

When the former exists in the electron path L, it means that blocking of the transmission channel has occurred, and when the former exists in the electron path U, it means that blocking of the transmission channel has not occurred.

That is, in [Equation 2] to [Equation 5], | pass> _e indicates that an electron is present in the electron path U and thus blocking of a transmission channel has not occurred, and | block> _e electrons exist in the electron path L This indicates that blocking of the transmission channel has occurred.

After performing the polarization of photons, the first device 100 provides each to a plurality of paths, and generates a message indicating the path of the photons according to whether a photon exists in each of the plurality of paths, thereby generating a second device 200 ).

In one embodiment, the first device 100 determines whether a photon exists in the first path or the second path, and according to the type of the detector of the path according to the determination result of the first component of the photon A message corresponding to the state and the state of the second component may be generated and provided to the second device 200.

The first device 100 will be described in more detail with reference to FIG. 3 below.

)를 전자에 적용한다. 이때, (파울리 연산자

)의 z는 오퍼레이터이고, m₁은 제1 장치(100)로부터 수신된 메시지 중 일부 정보일 수 있다. The second device 200 estimates the initial state of the photon based on the message received from the first device 100. To this end, the second device 200 determines a predetermined operator (Paulley operator) based on the message.

) To the former. At this time, (Paulian operator

) Z is an operator, and m ₁ may be some information among messages received from the first device 100.

Thereafter, the second device 200 estimates the initial state of the photon by applying an operator corresponding to the polarization state of the photon among the plurality of operators based on the message according to the bell type state of the photon.

In one embodiment, when the bell-type state of the photon is orthogonal, the second device 200 estimates the initial state of the photon after applying one of the plurality of operators to the former. At this time, as shown in [Table 2], a plurality of operators is U (m ₂ ) 와 {U1, U2}, and m ₂ means the rest of the information in the message. That is, the second device 200 may estimate the initial state of the photon by applying U1 or U2 to the former according to the photon's bell type state.

In another embodiment, when the bell-type state of the photon is a non-orthogonal state, the second device 200 defines any one of a plurality of predetermined states as a photon polarization state.

Thereafter, the second device 200 applies the minimum error state discrimination method U (m ₂ ) ∈ {A1, A2} to the former, and then an unambiguous state discrimination method USD U (m ₂ ) ∈ {S1, S2} Is applied to the former to estimate the initial state of the photon.

3 is a view for explaining the internal structure of the first device of FIG. 2.

Referring to Figure 3, the first device 100 is PBS1 (210), H-MCQZ gate 220, V-MCQZ gate 230, PBS ₂ (240), beam separator 250, PBS3 (260) And PBS ₄ (270).

The first device 100 performs the polarization of the photon by passing the first component H of the photon and reflecting the second component V, and then measures the path of the photon where the polarization is performed, and the A message corresponding to the measurement result is generated and provided to the second device 200.

To this end, PBS ₁ (210) passes through the first component (H) of the photon and reflects and outputs the second component (V) of the photon. The first component H and the second component V output from PBS ₁ 210 are respectively input to the H-MCQZ gate 220 and the V-MCQZ gate 230, and the H-MCQZ gate ( 220) and the photons output from V-MCQZ gate 230, respectively, are provided to PBS ₂ (240) and beam separator (250).

The photon output from the beam splitter 250 may exist in the first path (eg, the x path in FIG. 2) or the second path (eg, the y path in FIG. 2).

If, when the photon output from the beam splitter 250 is present in the first path, the former state is as shown in [Equation 8] below.

[Equation 8]

On the other hand, when the photon output from the beam splitter 250 exists in the second path, the state of the former is as shown in Equation 9 below.

[Equation 9]

Each photon output from the beam splitter 250 is provided to PBS3 260 through a first path and provided to PBS ₄ 270 through a second path. The PBS3 260 in the first path passes through the first component H of the photon and reflects the second component V of the photon and outputs it.

The first component H output from the PBS ₃ 260 in the first path is no longer provided to any component and ends in the first detector D ₁ , and the PBS ₃ (260) in the first path The second component V output from) is no longer provided to any component and ends at the second detector D ₂ .

PBS ₄ 270 in the second path passes through the first component H of the photon and reflects the second component V of the photon and outputs it. The first component H output from PBS ₄ 270 in the second path is no longer provided to any component and ends in the third detector D ₃ , and the PBS ₃ in the second path (260) The second component V output from) is no longer provided to any component and ends at the fourth detector D ₄ .

Accordingly, the first device 100 generates a different message corresponding to the type of the photon polarization state and the detector according to whether the photon exists in the first path or the second path, and thus the second device 200. To give.

In one embodiment, when the photon is present in the first path (eg, x path), the first device 100 is configured to detect the polarization state and detector of the photon present on the first path with reference to [Table 1]. The message corresponding to the type is extracted and provided to the second device 200.

For example, if the photon exists in the x path, the photon polarization state is | H> _P, and the type of detector is the first detector D ₁ , the message 00 is generated and provided. As another example, if the photon is present in the x path, the photon polarization state is | V> _P, and the type of detector is the second detector D ₂ , the message 01 is generated and provided.

In another embodiment, when the photon is present in the second path, the first device 100 extracts a message corresponding to the polarization state of the photon and the type of the detector in the second path with reference to [Table 1] Is provided to the second device 200.

For example, if the photon is present in the y path and the photon polarization state is | H> _P and the type of detector is the third detector (D ₃ ), a message 10 is generated and provided. As another example, if the photon is present in the y path, the photon polarization state is | V> _P, and the type of detector is the fourth detector D ₄ , a message 11 is generated and provided.

)를 전자에 적용할 수 있다. 이때, 미리 결정된 연산자(파울리 연산자

)의 z는 오퍼레이터이고, m₁은 제1 장치(100)로부터 수신된 메시지 중 일부 정보일 수 있다. Accordingly, the second device 200 may determine a predetermined operator (for example, a Pauli operator) based on some information (eg, m ₁ ) of the message received from the first device 100.

) Can be applied to the former. At this time, the predetermined operator (Paulley operator

) Z is an operator, and m ₁ may be some information among messages received from the first device 100.

[Table 1]

)를 전자에 적용한 후에 전자의 상태는 [수학식 10] 내지 [수학식 13]과 같다.As described above, the second device 200 determines a predetermined operator (Paulley operator) based on some information (eg, m ₁ ) of the message received from the first device 100.

) Is applied to the former, the states of the former are as shown in [Equation 10] to [Equation 13].

Thereafter, the second device 200 estimates the initial state of the photon by applying an operator corresponding to the polarization state of the photon among the plurality of operators based on the remaining information in the message according to the photon's bell type state. do.

At this time, as shown in [Table 2], a plurality of operators is U (m ₂ ) 와 {U1, U2}, and m ₂ means the rest of the information in the message. That is, the second device 200 may estimate the initial state of the photon by applying U1 or U2 to the former according to the photon's bell type state.

[Table 2]

If the second device 200 is in the orthogonal state, the photon's bell type state performs one of a plurality of operators and estimates the initial state of the photon. That is, the second device 200 extracts the photon polarization state from the message received from the first device 100, and selects an operator U (m ₂ ) corresponding to the photon polarization state from [Table 2]. Can be done.

For example, when the polarization state of the photon is the first component (| H> _p ), the second device 200 may select and perform the operator U1 among a plurality of operators, and the photon polarization state is the second configuration For the element (| V> _p ), it can be done by selecting the operator U2.

)가 적용된 후의 전자 상태를 각각 나타내는 [수학식 10] 내지 [수학식 13]은 하기의 [수학식 14] 내지 [수학식 17]과 같이 변경된다.As described above, when the bell-type state of the photon is in an orthogonal state, the second device 200 corresponds to an operator U1 corresponding to the polarization state of the photon among a plurality of operators based on the remaining information in the message according to the photon bell-type state. Or when U2) is applied to the former, a predetermined operator (Paulley operator)

), [Equation 10] to [Equation 13] respectively representing the electronic state after being applied are changed as shown in [Equation 14] to [Equation 17] below.

U1 and U2 in [Equation 14] to [Equation 17] are as shown in [Equation 18] and [Equation 19] below.

On the other hand, the second device 200, when the photon bell type state is a non-orthogonal state, the minimum error state discrimination method U (m ₂ ) ∈ {A1, A2} or the unambiguous state discrimination method USD U (m ₂ ) ∈ Execute {S ₁ , S ₂ }.

There are four general bell-type states, as shown in [Equation 20] to [Equation 23] below.

)를 전자에 적용한 후, [수학식 24] 및 [수학식 25]와 같이 제1 구성 요소(|H>_p) 및 제2 구성 요소 (|V>_p) 각각에 대해 미리 결정된 복수의 상태 중 어느 하나의 상태를 상기 제1 구성 요소(|H>_p)의 상태 및 상기 제2 구성 요소(|V>_p)의 상태를 정의한다. The second device 200 may determine a predetermined operator based on some information (eg, m ₁ ) of the message received from the first device 100 (

) Is applied to the former, and among the plurality of predetermined states for each of the first component (| H> _p ) and the second component (| V> _p ), such as [Equation 24] and [Equation 25] Any one state defines the state of the first component (| H> _p ) and the state of the second component (| V> _p ).

으로 결정하고 [수학식 25]를 기초로 광자의 |V>_p의 상태를

으로 결정할 수 있다.For example, the second device 200 determines the state of the first component of the photon (| H> _p ) based on [Equation 24].

And determine the state of | V> _p of photons based on [Equation 25]

You can decide.

으로 결정하고 [수학식 25]를 기초로 광자의 |V>_p의 상태를

으로 결정할 수 있다. For another example, the second device 200 may determine the state of | H> _p of photons based on [Equation 24].

And determine the state of | V> _p of photons based on [Equation 25]

You can decide.

또는

으로 결정하거나 광자의 제1 구성 요소(|V>_p)의 상태를

또는

으로 결정할 수 있다.That is, the second device 200 displays the state of the first component of the photon (| H> _p ).

or

Or the state of the first component of the photon (| V> _p )

or

You can decide.

[Equation 24]

는 [수학식 20]을 기초로 생성되었으며,

는 [수학식 21]을 기초로 생성되었다.At this time,

Was created based on [Equation 20],

Was created based on [Equation 21].

[Equation 25]

는 [수학식 22]을 기초로 생성되었으며,

는 [수학식 23]을 기초로 생성되었다.At this time,

Was created based on [Equation 22],

Was created based on [Equation 23].

Then, the second device 200 applies the minimum error state discrimination method U (m ₂ ) ∈ {A1, A2} to the former. That is, the second device 200 applies U (m ₂ ) = A ₁ as shown in [Equation 26] for the state of the first component of the photon (| H> _p ), and the second component of the photon For the state of (| V> _p ), U (m ₂ ) = A ₂ is applied as in [Equation 26].

[Equation 26]

는 하기의 [수학식 27]와 같이 각각의 j에 해당한다.[Equation 26] in each

Is corresponding to each j as shown in [Equation 27] below.

[Equation 27]

는 하기의 [수학식 28]과 같고,

는 하기의 [수학식 29]와 같다. [Equation 27]

Is equal to [Equation 28] below,

Is as shown in [Equation 29] below.

: 광자의 제1 구성 요소(|H>_p)의 상태,

: State of the first component of the photon (| H> _p ),

: 광자의 제2 구성 요소(|V>_p)의 상태

: State of the second component of the photon (| V> _p )

[Equation 32]

,

,

: 최적의 사형 측정의 집합

: Set of optimal death penalty measurements

[Equation 33]

[Equation 34]

일 때

는 j 번째 출력이 획득될 확률이고, 광자의 초기 상태 추정은 제5 디텍터(D₅) 또는 제6 디텍터(D₆)에서 [수학식 34]의 1 및 3 또는 2 및 4의 추정 결과로서 출력되어 종료된다. The state of the photon

when

Is the probability that the j-th output is obtained, and the initial state estimation of the photon is output as the estimation result of 1 and 3 or 2 and 4 of [Equation 34] in the fifth detector (D ₅ ) or the sixth detector (D ₆ ). And ends.

[Equation 35]

If the bell type is orthogonal, Pinc is 0.

Thereafter, the second device 200 applies the unambiguous state discrimination method USD U (m ₂ ) ∈ {S1, S2} to the former. That is, the second device 200 selects one of U (m ₂ ) ∈ {S1, S2} as shown in [Table 3] and applies it to the former to identify the four general bell types. Estimate.

[Table 3]

에 의해 실행된다. That is, the second device 200, that is, the second device 200 applies USD U (m ₂ ) = S1 to the state of the first component of the photon (| H> _p ), and the second of the photon For the state of the component (| V> _p ), USD U (m ₂ ) = S2 applies. Each USD has 3 POVM operators with [Equation 36]

Is executed by

[Equation 36]

I: identification operator,

i: set to 1 for the first component of the photon (| H> _P ) or 2 for the second component of the photon (| V> _P ),

:

에 해당하는 POVM 오퍼레이터

:

Corresponding POVM operator

,

,

,

,

[Equation 40]

4 is a flowchart for explaining an embodiment of a method for identifying a quantum bell state according to the present invention.

Referring to FIG. 4, the first device 100 executes polarization of photons and provides each to a plurality of paths (step S410).

The first device 100 generates a message indicating the path of the photon according to whether a photon exists in each of the plurality of paths (step S415) and provides it to the second device 200 (step S420).

In one embodiment of step S420, the first device 100, when the photon is present in the first path (eg, x path), the photon present on the first path with reference to [Table 1] above The message corresponding to the polarization state and the detector is extracted and provided to the second device 200.

For example, if the photon exists in the x path, the photon polarization state is | H> _P, and the type of detector is the first detector D ₁ , the message 00 is generated and provided. As another example, if the photon is present in the x path, the photon polarization state is | V> _P, and the type of detector is the second detector D ₂ , the message 01 is generated and provided.

In another embodiment of step S420, when the photon is present in the second path, the first device 100 corresponds to the polarization state of the photon and the type of the detector in reference to [Table 1]. The extracted message is provided to the second device 200.

For example, if the photon is present in the y path and the photon polarization state is | H> _P and the type of detector is the third detector (D ₃ ), a message 10 is generated and provided. As another example, if the photon is present in the y path, the photon polarization state is | V> _P, and the type of detector is the fourth detector D ₄ , a message 11 is generated and provided.

The second device 200 applies a predetermined operator to the former based on the message (step S430).

The second device 200 estimates the initial state of the photon by applying an operator corresponding to the polarization state of the photon among the plurality of operators based on the message according to the bell type state of the photon (step S440). .

In one embodiment of step S440, when the bell-type state of the photon is orthogonal, the second device 200 is connected to the first component according to the polarization state of the photon extracted from the message among the plurality of operators. An initial state of the photon may be estimated by applying a corresponding operator or an operator corresponding to the second component to the former.

As described above, although the present invention has been described by limited embodiments and drawings, the present invention is not limited to the above embodiments, and various modifications and modifications from these descriptions will be made by those skilled in the art to which the present invention pertains. Deformation is possible. Accordingly, the spirit of the present invention should be understood only by the claims set forth below, and all equivalents or equivalent modifications thereof will be said to fall within the scope of the spirit of the present invention.

150: V(H)-QZ 게이트
210: PBS₁
220: H-MCQZ 게이트
230: V-MCQZ 게이트
240: PBS₂
250: 빔 분리기
260: PBS₃
270: PBS₄
200: 제2 장치100: first device
110: optical circulator
120: H (V) -QZ gate
130: switch mirror
140:

150: V (H) -QZ gate
210: PBS ₁
220: H-MCQZ gate
230: V-MCQZ gate
240: PBS ₂
250: beam separator
260: PBS ₃
270: PBS ₄
200: second device

Claims (5)

Providing a plurality of paths to the plurality of paths after the first device performs polarization of the photons;
Generating, by the first device, a message indicating a path of the photon according to whether a photon exists in each of the plurality of paths and providing the message to the second device;
Applying, by the second device, a predetermined operator to the former based on the message;
And the second device estimating the initial state of the photon by applying an operator corresponding to the polarization state of the photon among the plurality of operators based on the message according to the bell type state of the photon. Characterized by
Quantum bell state identification method.
According to claim 1,
Generating a message indicating the path of the photon and providing it to the second device is
The first device determines whether a photon exists in the first path or the second path, and according to the type of the detector of the corresponding path according to the determination result, the state of the first component and the second component of the photon And generating and providing a message corresponding to the state to the second device.
Quantum bell state identification method.
According to claim 2,
Estimating the initial state of the photon is
When the photon's bell type state is an orthogonal state, the operator corresponding to the first component or the operator corresponding to the second component may be determined according to the polarization state of the photon extracted from the message among the plurality of operators. And applying the former to estimate the initial state of the photon.
Quantum bell state identification method.
According to claim 2,
Estimating the initial state of the photon is
When the photon's bell type state is an orthogonal state, the state of the first component and the second component of one of a plurality of predetermined states for each of the first component and the second component are Characterized by defining as a state
Quantum bell state identification method.
The method of claim 4,
Estimating the initial state of the photon is
Characterized in that the initial state of the photon is estimated by applying a minimum error state discrimination method and an unambiguous state discrimination method to the former for each of the first component and the second component
Quantum bell state identification method.

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