CN104601248B - Method for remote preparation of quantum state based on multi-party joint operation based on single atom - Google Patents

Abstract

A kind of multi-party joint based on monatomic operation remotely prepares the method for quantum state, wherein making the monatomic quantum bit state of two sender's remote assistances, one recipient's Restore Secret：| Φ ＞=α | g ＞+β | e ＞；Wherein | g ＞ l | e ＞ represent the ground state and excitation state of Two level atom respectively, and parameter alpha, β is real number, and meet condition α²+β²=1；And parameter alpha, β describes all information of secret quantum bit, and all information of secret quantum bit are split as two parts, possessed respectively by two senders.The information that first sender possesses is { α₁, β₁, the information that the second sender possesses is { α₂, β₂}；The W type Quantum Entangled States being made up of three Two level atoms are shared between two senders and a recipientWherein the first atom belongs to the first sender, and the second atom belongs to the second sender, and the 3rd atom belongs to recipient.

Description

Method for remote preparation of quantum state based on multi-party joint operation based on single atom

technical field

The present invention relates to the field of quantum information and communication network, more specifically, the present invention relates to a multi-party joint remote preparation method of quantum state based on single atom operation.

Background technique

Quantum communication is a new type of communication that has emerged in recent years. By encoding information into a physical system with quantum properties, using the quantum properties of the system state, such as quantum entanglement, measurement collapse, and quantum state non-cloning, etc., the quantum communication process is safer, more efficient, and anti-interference than classical communication. With the deepening of research on quantum communication networks, various quantum communication methods have been proposed to solve communication problems such as information transmission, information encryption, key distribution, and secret sharing.

Suppose that after some information processing, for example, after a quantum secret sharing, the classical information describing the content of a secret qubit is split and distributed to different nodes of the quantum network. That is to say, each node only has a part of the information of the secret qubit state; no node has all the information of the secret qubit, and can independently restore the information of the secret qubit. The question now is how to be able to reconstruct the secret information in a new node. For this reason, a multi-party joint remote preparation method for quantum states is proposed in the prior art. These methods respectively use different quantum entanglement states as the transmission channel of quantum information to complete the joint remote preparation task of different types of qubit states.

However, these research works only proposed a multi-party joint remote preparation method for qubit states from the mathematical level, but did not propose a practically operable solution for specific physical systems. Moreover, the experimental schemes proposed by a small number of researchers all use single photons as the carrier of information, and single photons are often easily affected by the environment and annihilated in actual operation.

At present, there is almost no discussion on the method of joint remote preparation of quantum states for specific physical systems, no consideration of how to realize this process in the actual physical world, and no discussion of whether it is enforceable. A handful of physics programs are explored primarily in photonic systems. Although the photon transmission speed is fast, the decoherence time is short, and it is easy to annihilate in the actual physical environment. Moreover, in the process of remote preparation of quantum states, it is not necessary to transmit the information carrier, but to properly operate the information carrier. It can be seen that the photonic system is not an ideal physical system for joint remote preparation of quantum states.

Contents of the invention

The technical problem to be solved by the present invention is to solve the above-mentioned defects in the prior art, and from the perspective of practical operability, a two-level atom is proposed as an information carrier, and the mutual interaction between a single two-level atom and the classical electromagnetic field is proposed. The function is to use the three-atom W-type entangled state as the transmission channel of quantum information to complete the method of remote preparation of the secret single-qubit state with the participation of two senders and one receiver.

In order to achieve the above technical purpose, according to the present invention, a multi-party joint remote preparation method for quantum states based on single-atom operations is provided, in which two senders remotely assist a receiver to restore the secret single-atom qubit state:

|φ>=α|g>+β|e>;

where |g>,|e> represent the ground state and excited state of two-level atoms respectively, the parameters α, β are real numbers, and the condition α ² + β ² = 1 is satisfied; and the parameters α, β describe all secret qubits Information, all information of the secret qubit is split into two parts, which are owned by the two senders respectively.

Preferably, the information owned by the first sender is {α ₁ , β ₁ }, and the information owned by the second sender is {α ₂ , β ₂ }; A W-type quantum entangled state composed of two-level atoms

Where the first atom belongs to the first sender, the second atom belongs to the second sender, and the third atom belongs to the receiver.

Preferably, the two senders respectively establish a quantum communication channel and a classical communication channel with the receiver.

Preferably, there is no communication link between the two senders.

Preferably, the method comprises the steps of:

Step 1: The two senders respectively let their own atoms pass through a classical electromagnetic field. The frequency of the classical electromagnetic field should resonate with the transition frequency between the ground state and the excited state of the atom; The information of α, β {α _i , β _i }, regulates the complex amplitude of the classical electromagnetic field The coupling coefficient Ω _i between the atom and the classical field, and the flight time t _i of the atom in the classical field, so that the following conditions are satisfied:

in

The second step: After the first step is completed, the quantum state of the system composed of three atoms will evolve to the following form:

At this time, the two senders respectively measure the atomic basis vectors they own, judge that the atom is in the ground state |g> or the excited state |e>, and send the measurement results to the receiver through the classical channel;

The third step: the receiver judges the state of the third atom based on the measurement results from the two senders and the splitting method of the parameters α and β, so as to determine whether the secret single-qubit state |φ> is restored.

Preferably, in the third step, if the splitting of parameters α and β conforms to the following relationship,

Then when the classical information from the two senders shows that both the first atom and the second atom are in the ground state, that is, the state of the two atoms is |g> ₁ |g> ₂ , it is judged that the third atom is in the secret single-qubit state. Preferably, in the third step, if the splitting of parameters α and β conforms to the following relationship,

Then when the classical information from the two senders shows that the first atom is in the ground state and the second atom is in the excited state, that is, the state of the two atoms is |g> ₁ |e> ₂ , it is judged that the third atom is in the secret single quantum bit state.

Preferably, in the third step, if the splitting of parameters α and β conforms to the following relationship,

Then when the classical information from the two senders shows that the first atom is in the excited state and the second atom is in the ground state, that is, the state of the two atoms is |e> ₁ |g> ₂ , it is judged that the third atom is in the secret single quantum bit state.

Preferably, in the third step, if the splitting of parameters α and β conforms to the following relationship,

Then when the classical information from the two senders shows that the first atom and the second atom are both in the excited state, that is, the state of the two atoms is |e> ₁ |e> ₂ , it is judged that the third atom is in the secret single-qubit state .

The invention proposes a method that uses two-level atoms as information carriers and can recover secret information after quantum secret sharing. In this method, each sender only has a part of the secret information, and the secret information is transmitted through the quantum channel, so it has good security; the technology involved in this method is mainly the relatively mature use of The classical electromagnetic field interacts with a single two-level atom to realize the technology of manipulating the state of the atom, which has practical operability; at the same time, the three-atom W-type entangled state is used as the quantum channel, which can better overcome the influence of environmental noise , with strong anti-interference.

Description of drawings

A more complete understanding of the invention, and its accompanying advantages and features, will be more readily understood by reference to the following detailed description, taken in conjunction with the accompanying drawings, in which:

Fig. 1 schematically shows a flow chart of a method for multi-party joint remote preparation of quantum states based on single-atom operations according to a preferred embodiment of the present invention.

It should be noted that the accompanying drawings are used to illustrate the present invention, but not to limit the present invention. Note that drawings showing structures may not be drawn to scale. And, in the drawings, the same or similar elements are marked with the same or similar symbols.

detailed description

In order to make the content of the present invention clearer and easier to understand, the content of the present invention will be described in detail below in conjunction with specific embodiments and accompanying drawings.

According to the preferred embodiment of the present invention, the method for multi-party joint remote preparation of quantum states based on single-atom operation is based on the interaction between a single two-level atom and a classical electromagnetic field. Among them, (1) multiple senders at different nodes only know part of the information of the secret quantum state, but not all information, so any sender cannot disclose the secret information; (2) only when multiple senders The secret quantum state can only be re-established in a third party under the cooperation of the parties. The absence of any party will lead to the failure of the preparation process, which further guarantees the security of the secret quantum state; (3) The channel for quantum information transmission is three The W-type entanglement between atoms makes this method better resistant to environmental noise; (4) The two senders share information on the secret quantum state, and the way the information is distributed between the two is related to the preparation of the secret quantum state. Success or failure; (5) The state of the atom represents information. Utilizing the interaction between the two-level atoms and the classical electromagnetic field, the manipulation of the atomic state can be realized, that is, the processing of information can be completed.

The present invention involves three separate participants (two senders and one receiver), enabling the two senders to remotely assist a receiver in recovering the secret single-atom qubit state:

|φ>=α|g>+β|e>

in represent the ground state and the excited state of the two-level atoms respectively, the parameters α and β are real numbers, and the condition α ² +β ² =1 is satisfied. parameter Describes all the information of the secret qubits, which are split into two parts, owned by the two senders respectively. It may be assumed that the information owned by the first sender Alice is {α ₁ , β ₁ }, and the information owned by the second sender Bob is {α ₂ , β ₂ }. Two senders and one receiver share a W-type quantum entanglement state composed of three two-level atoms

Among them, the first atom 1 belongs to the first sender Alice, the second atom 2 belongs to the second sender Bob, and the third atom 3 belongs to the receiver Carol. The two senders have established a quantum communication channel and a classical communication channel with the receiver respectively; in order to ensure the security of the secret qubit, there is no communication link between the two senders.

In order to restore the secret single-qubit state, the specific steps of the three participants are shown in Figure 1, which schematically shows the flow of the method for multi-party joint remote preparation of quantum states based on single-atom operations according to a preferred embodiment of the present invention picture.

As shown in Figure 1, the multi-party joint remote preparation method for quantum states based on single-atom operations according to a preferred embodiment of the present invention includes:

The first step S1: the two senders respectively let their own atoms pass through a classical electromagnetic field, and the frequency of the classical electromagnetic field should resonate with the transition frequency between the ground state and the excited state of the atom. The two senders adjust the complex amplitude of the classical electromagnetic field according to their own information about the parameters α, β {α _i , β _i } The coupling coefficient Ω _i between the atom and the classical field, and the flight time t _i of the atom in the classical field, so that the following conditions are satisfied:

in

The second step S2: After the first step S1 is completed, the quantum state of the system composed of three atoms will evolve to the following form:

At this time, the two senders measure the atomic basis vectors they own respectively, judge that the atom is in the ground state |g> or the excited state |e>, and send the measurement results to the receiver through the classical channel.

The third step S3: there are four different possible situations for the measurement results of the two senders, and corresponding to each measurement result, the third atom 3 will collapse into different quantum states. The receiver Carol, based on the classical information (measurement results) from the two senders and the splitting method of the parameters α and β, can judge the state of the third atom 3 she has mastered, and thus know the secret single qubit Whether the state |φ> has been recovered.

If the splitting of parameters α, β conforms to the following relationship,

Then when the classic information from the two senders shows that the first atom 1 and the second atom 2 are in the ground state, that is, the state of the two atoms is |g> ₁ |g> ₂ , Carol can judge that the third atom 3 is in the secret state single qubit state.

If the splitting of parameters α, β conforms to the following relationship,

Then when the classical information from the two senders shows that the first atom 1 is in the ground state and the second atom 2 is in the excited state, that is, the states of the two atoms are |g> ₁ |e> ₂ , Carol can judge that the third atom 3 is in a secret single-qubit state.

If the splitting of parameters α, β conforms to the following relationship,

Then when the classical information from the two senders shows that the first atom 1 is in the excited state and the second atom 2 is in the ground state, that is, the states of the two atoms are |e> ₁ |g> ₂ , Carol can judge that the third atom 3 is in a secret single-qubit state.

If the splitting of parameters α, β conforms to the following relationship,

Then when the classical information from the two senders shows that both the first atom 1 and the second atom 2 are in an excited state, that is, the state of the two atoms is |e> ₁ |e> ₂ , Carol can judge that the third atom 3 is in Secret single-qubit states.

If the splitting of parameters α and β does not conform to any of the above relationships, no matter what the measurement results of the first atom 1 and the second atom 2 are, the recovery of the secret single qubit cannot be completed.

The present invention has at least the following advantages:

(1) Many related research results in the past only discussed how to achieve remote reconstruction of a quantum state by multiple senders working together from the mathematical level. The difference is that in a specific physical system such as a two-level atom and a classical light field, we have designed a method for the joint remote preparation of a single atomic state involving three parties. The interaction between atoms and classical fields is already a very mature technology in the laboratory, so this method has good operability;

(2) Compared with the photonic system, the quantum state of the atomic system has a longer decoherence time, or is more stable, so it is usually considered as an ideal fixed bit. This makes it more suitable than photonics for joint remote fabrication processes. Because in the process of remote preparation of quantum states, the physical system as the information carrier does not need to be transmitted to other locations, but only needs to be operated locally. Therefore, we use two-level atoms as the carrier of information;

(3) The current research on the three-body entanglement shows that there are only two unequal ways of entanglement among the three quantum systems, one is the GHZ type, and the other is the W type. Relatively speaking, W-type entanglement exhibits higher robustness and stronger non-classical characteristics, which makes it considered as an ideal entanglement resource in quantum information processing. The method adopts a W-type entangled state composed of three atoms as a channel for quantum information transmission, which improves the anti-interference ability of the communication process.

In addition, it should be noted that, unless otherwise specified or pointed out, the terms “first”, “second”, “third” and other descriptions in the specification are only used to distinguish each component, element, step, etc. in the specification, and It is not used to represent the logical relationship or sequential relationship between various components, elements, and steps.

It can be understood that although the present invention has been disclosed above with preferred embodiments, the above embodiments are not intended to limit the present invention. For any person skilled in the art, without departing from the scope of the technical solution of the present invention, the technical content disclosed above can be used to make many possible changes and modifications to the technical solution of the present invention, or be modified to be equivalent to equivalent changes. Example. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention, which do not deviate from the technical solution of the present invention, still fall within the protection scope of the technical solution of the present invention.

Claims (8)

1. a kind of multi-party joint based on monatomic operation remotely prepares the method for quantum state, wherein making two senders remotely assist Help the monatomic quantum bit state of recipient's Restore Secret：

| φ ＞=α | g ＞+β | e ＞；

Wherein | g ＞ | e ＞ represent the ground state and excitation state of Two level atom respectively, and parameter alpha, β is real number, and meet condition α²+β² =1；And parameter alpha, β describes all information of secret quantum bit, and all information of secret quantum bit are split as two Individual part, is possessed by two senders respectively；

Methods described comprises the steps：

First step：Two senders allow the atom oneself possessed through a Classical Electromagnetic Field respectively, Classical Electromagnetic Field Jump frequency resonance between frequency and atomic ground state and excitation state；Two senders according to each being possessed on parameter alpha, β information { α_i,β_i, adjust the complex amplitude of Classical Electromagnetic FieldCoefficient of coup Ω between atom and Classical Fields_i, with And flight time t of the atom in Classical Fields_i, so as to meet following condition：

Wherein θ_i=Ω_i|A_i|t_i；

Second step：Complete after first step, the quantum state for the system that three atoms are constituted will develop to following form：

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>|</mo> <mi>&amp;Psi;</mi> <mo>&gt;</mo> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mrow> <mn>3</mn> <mrow> <mo>(</mo> <msubsup> <mi>&amp;alpha;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;beta;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msubsup> <mi>&amp;alpha;</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;beta;</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mrow> </msqrt> </mfrac> <mo>{</mo> <mo>|</mo> <mi>g</mi> <mi>g</mi> <msub> <mo>&gt;</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;beta;</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>&amp;beta;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>|</mo> <mi>g</mi> <msub> <mo>&gt;</mo> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> <mo>|</mo> <mi>e</mi> <msub> <mo>&gt;</mo> <mn>3</mn> </msub> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mo>|</mo> <mi>g</mi> <mi>e</mi> <msub> <mo>&gt;</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>&amp;beta;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;beta;</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>|</mo> <mi>g</mi> <msub> <mo>&gt;</mo> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;beta;</mi> <mn>2</mn> </msub> <mo>|</mo> <mi>e</mi> <msub> <mo>&gt;</mo> <mn>3</mn> </msub> <mo>&amp;rsqb;</mo> <mo>+</mo> <mo>|</mo> <mi>e</mi> <mi>g</mi> <msub> <mo>&gt;</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>&amp;lsqb;</mo> <mo>(</mo> <mo>-</mo> <msub> <mi>&amp;beta;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;beta;</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>&amp;beta;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> <mo>)</mo> <mo>|</mo> <mi>g</mi> <msub> <mo>&gt;</mo> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> <mo>|</mo> <mi>e</mi> <msub> <mo>&gt;</mo> <mn>3</mn> </msub> <mo>&amp;rsqb;</mo> <mo>+</mo> <mo>|</mo> <mi>e</mi> <mi>e</mi> <msub> <mo>&gt;</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>&amp;beta;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>&amp;beta;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;beta;</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>|</mo> <mi>g</mi> <msub> <mo>&gt;</mo> <mn>3</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;beta;</mi> <mn>2</mn> </msub> <mo>|</mo> <mi>e</mi> <msub> <mo>&gt;</mo> <mn>3</mn> </msub> <mo>&amp;rsqb;</mo> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>

Now, two senders measure to its own atom basic vector respectively, judge that atom is in ground state | and g ＞ swash Send out state | e ＞, and measurement result is sent to recipient by classical channel；

Third step：Recipient judges the according to the measurement result from two senders and incorporating parametric α, β fractionation mode Three atom state in which, so that it is determined that secret single quantum bit state | whether φ ＞ are resumed.

2. the method that the multi-party joint according to claim 1 based on monatomic operation remotely prepares quantum state, its feature It is, the information that the first sender possesses is { α₁, β₁, the information that the second sender possesses is { α₂, β₂}；Two senders and The W type Quantum Entangled States being made up of three Two level atoms are shared between one recipient

<mrow> <mo>|</mo> <mi>&amp;Psi;</mi> <mo>&gt;</mo> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mn>3</mn> </msqrt> </mfrac> <msub> <mrow> <mo>(</mo> <mo>|</mo> <mi>g</mi> <mi>g</mi> <mi>e</mi> <mo>&gt;</mo> <mo>+</mo> <mo>|</mo> <mi>g</mi> <mi>e</mi> <mi>g</mi> <mo>&gt;</mo> <mo>+</mo> <mo>|</mo> <mi>e</mi> <mi>g</mi> <mi>g</mi> <mo>&gt;</mo> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </msub> <mo>,</mo> </mrow>

Wherein the first atom belongs to the first sender, and the second atom belongs to the second sender, and the 3rd atom belongs to recipient.

3. the method that the multi-party joint according to claim 1 or 2 based on monatomic operation remotely prepares quantum state, it is special Levy and be, two senders establish quantum communications channel and classical communication channel between recipient respectively.

4. the method that the multi-party joint according to claim 1 or 2 based on monatomic operation remotely prepares quantum state, it is special Levy and be, do not write to each other between two senders.

5. the method that the multi-party joint according to claim 1 or 2 based on monatomic operation remotely prepares quantum state, it is special Levy and be, in third step, if to parameter alpha, β fractionation meets following relation,

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mi>&amp;beta;</mi> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> </mfrac> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;beta;</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <msub> <mi>&amp;alpha;&amp;alpha;</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>&amp;beta;&amp;beta;</mi> <mn>1</mn> </msub> </mrow> <msubsup> <mi>&amp;alpha;</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced>

Then when the classical information from two senders shows the first atom and the second atom all in ground state, i.e., two atoms State be | g ＞₁| g ＞₂, judge that the 3rd atom is in secret single quantum bit state.

6. the method that the multi-party joint according to claim 1 or 2 based on monatomic operation remotely prepares quantum state, it is special Levy and be, in third step, if to parameter alpha, β fractionation meets following relation,

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;alpha;&amp;alpha;</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;beta;&amp;beta;</mi> <mn>1</mn> </msub> </mrow> <msubsup> <mi>&amp;alpha;</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mfrac> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;beta;</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mi>&amp;beta;</mi> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced>

Then when the classical information from two senders shows that the first atom is in excitation state in ground state, and the second atom, The state of i.e. two atoms is | g ＞₁| e ＞₂, judge that the 3rd atom is in secret single quantum bit state.

7. the method that the multi-party joint according to claim 1 or 2 based on monatomic operation remotely prepares quantum state, it is special Levy and be, in third step, if to parameter alpha, β fractionation meets following relation,

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mi>&amp;beta;</mi> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> </mfrac> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;beta;</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <msub> <mi>&amp;alpha;&amp;alpha;</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>&amp;beta;&amp;beta;</mi> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;beta;</mi> <mn>1</mn> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced>

Then when the classical information from two senders shows that the first atom is in ground state in excitation state, and the second atom, The state of i.e. two atoms is | e ＞₁| g ＞₂, judge that the 3rd atom is in secret single quantum bit state.

8. the method that the multi-party joint according to claim 1 or 2 based on monatomic operation remotely prepares quantum state, it is special Levy and be, in third step, if to parameter alpha, β fractionation meets following relation,

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;alpha;</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;alpha;&amp;alpha;</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>&amp;beta;&amp;beta;</mi> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> <msub> <mi>&amp;beta;</mi> <mn>1</mn> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;beta;</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mi>&amp;beta;</mi> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced>

Then when the classical information from two senders shows the first atom and the second atom all in excitation state, i.e., two originals Son state be | e ＞₁| e ＞₂, judge that the 3rd atom is in secret single quantum bit state.