CN105471515B - The long-range method for preparing quantum state of joint based on three atom GHZ states - Google Patents

Abstract

The invention provides a method for joint remote preparation of quantum states based on triatomic GHZ states. The first sender and the second sender remotely assist a receiver to recover the secret single-atom qubit state |Φ＞=α|g＞+β|e＞, where |g＞ and |e＞ represent two-level atoms respectively The ground state and excited state of , the parameters α and β are real numbers, and the condition α ² + β ² = 1 is satisfied; moreover, the parameters α and β describe all the information of the secret qubit; the parameters α and β are split into two parts , are owned by two senders respectively, so that the information owned by the first sender {α ₁ , β ₁ }, the information owned by the second sender {α ₂ , β ₂ }; the first sender, the second sender Share a GHZ-type quantum entangled state consisting of three two-level atoms with a recipient Wherein the first atom 1 belongs to the first sender, the second atom 2 belongs to the second sender, and the third atom 3 belongs to the receiver.

Description

Method for joint remote preparation of quantum state based on triatomic GHZ state

technical field

The present invention relates to the field of quantum information and communication network, more specifically, the present invention relates to a method for joint remote preparation of quantum state based on triatomic GHZ state.

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 recover the information of the secret qubit. The question now is how to be able to reconstruct the secret information in a new node. To this end, a multi-party joint remote preparation method for quantum states was proposed (see references [1]-[10]). These methods respectively use different quantum entangled states as the transmission channels of quantum information to complete the joint remote preparation 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. The experimental schemes proposed by a small number of researchers (see references [11][12]) all use single photons as information carriers, 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.

Reference list:

[1] Xia Y., Song J., Song H.S., Multiparty remote state preparation, J. Phys. B: At. Mol. Opt. Phys. 40, 3719 (2007).

[2]An N.B.and Kim J.,Joint remote state preparation,J.Phys.B:At.Mol.Opt.Phys.41,095501(2008).

[3] Hou K., Wang J., Lu Y-L, Shi S-H, Joint Remote Preparation of a Multipartite GHZ-class State, Int. J. Theor. Phys. 48, 2005 (2009)

[4]An N.B., Joint remote state preparation via W and W-type states, Opt.Commun.283, 4113(2010)

[5] Chen Q-Q, Xia Y., Song J. and An N.B. Joint remote state preparation of a W-type state via W-type states, Phys. Lett. A 374 4483, (2010).

[6]An N.B., Kim J.Joint remote preparation of a general two-qubitstate, J.Phys.B: At.Mol.Opt.Phys.42, 125501(2009).

[7] Luo M-X, Chen X-B, Ma S-Y, Niu X-X, Yang Y-X, Joint remote preparation of an arbitrary three-qubit state, Opt. Commun. 283, 4796 (2010).

[8] Wang Z-y, Highly efficient remote preparation of an arbitrary three-qubit state via a four-qubit cluster state and an EPR state, QuantumInf. Process 12, 1321 (2013).

[9] Peng J-Y, Luo M.X., Mo Z-W, Joint remote state preparation of arbitrary two-particle states via GHZ-type states, Quantum Inf. Process 12, 2325(2013).

[10]Liao Y-M,Zhou P.,Qin X-C,He Y-H,Efficient joint remote preparation of an arbitrary two-qubit state via cluster and cluster-typestates,Quantum Inf.Process 13,615(2014).

[11] Xia Y., Song J., Song H.S. and Guo J.L., Multiparty remote state preparation with linear optical elements, Int.J.Quantum Inf.61127, (2008)

[12] Luo, M.X., et al., Experiment architecture of joint remote state preparation, Quantum Inf. Process 11, 751 (2012).

Contents of the invention

The technical problem to be solved by the present invention is to provide a method for joint remote preparation of quantum states based on three-atom GHZ states in view of the above-mentioned defects in the prior art. Among them, the present invention starts from practical operability and proposes a two-level atom as an information carrier, using the interaction between a single two-level atom and a classical electromagnetic field, and using a three-atom GHZ-type entangled state as a quantum information carrier. The transmission channel is a method for remotely preparing a 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 method for joint remote preparation of quantum states based on the three-atom GHZ state is provided, which is used to enable the first sender and the second sender to remotely assist a receiver to recover the secret single atom The qubit state |Φ＞=α|g＞+β|e＞, where |g＞ and |e＞ represent the ground state and excited state of two-level atoms respectively, the parameters α and β are real numbers, and the condition α ² + β ² =1; moreover, parameters α and β describe all the information of the secret qubit; parameters α and β are split into two parts, which are owned by two senders respectively, so that the information owned by the first sender { α ₁ , β ₁ }, the information owned by the second sender {α ₂ , β ₂ }; the first sender, the second sender and a receiver share a GHZ composed of three two-level atoms type quantum entanglement Wherein the first atom 1 belongs to the first sender, the second atom 2 belongs to the second sender, and the third atom 3 belongs to the receiver.

Preferably, the first sender and the second sender respectively establish a quantum communication channel and a classical communication channel with the receiver.

Preferably, there is no communication link between the first sender and the second sender.

Preferably, the method for joint remote preparation of quantum states based on the triatomic GHZ state includes:

The first step: the first sender and the second sender 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 information about the parameters α and 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:

where θ _i =Ω _i |A _i |t _i ;

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 first sender and the second sender respectively measure the atoms they own, judge that the atoms are 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 3 held by the receiver based on the classical information from the two senders and the splitting method of the parameters α and β, so as to learn the secret single-qubit state| Φ＞Whether to be recovered.

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

α ₁ α ₂ =α, β ₁ β ₂ =β, then perform the following steps:

When the classical information from the first sender and the second sender shows that both the first atom 1 and the second atom 2 are in the ground state, that is, the states of the two atoms are |g> ₁ |g> ₂ , the receiver judges that the third Atom 3 is in a secret single-qubit state;

When the classical information from the first sender and the second sender shows that the first atom 1 and the second atom 2 are in the excited state at the same time, that is, the states of the two atoms are |e> ₁ |e> ₂ , the receiver sets the first Triatom 3 passes through a classical electromagnetic field, modulating the complex amplitude of the classical electromagnetic field The coupling coefficient Ω ₃ between the atom and the classical field, and the flight time t ₃ of the atom in the classical field make Ω ₃ |A ₃ |t ₃ =π/2, thereby converting the third atom 3 into a secret single-qubit state;

Preferably, in the third step, if the splitting of parameters α and β conforms to the relation:

Then perform the following steps:

When the classical information from the first sender and the second sender 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 , the receiver judges The third atom 3 is in a secret single-qubit state;

When the classical information from the two senders shows that the first atom 1 and the second atom 2 are both in the ground state, that is, the states of the two atoms are |e> ₁ |g> ₂ , the receiver makes the third atom 3 go through a Classical Electromagnetic Fields, Regulating the Complex Amplitude of Classical Electromagnetic Fields The coupling coefficient Ω ₃ between the atom and the classical field, and the flight time t ₃ of the atom in the classical field make Ω ₃ |A ₃ |t ₃ =π/2, Thereby converting the third atom 3 into a secret single-qubit state.

Therefore, the present 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. In the method of the present invention, the technique of manipulating the atomic state is realized by using the classical electromagnetic field to interact with a single two-level atom, which has practical operability; at the same time, the three-atom GHZ type entangled state is used as the quantum channel, which can Improving communication efficiency and making it more convenient in operation.

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 joint remote preparation of quantum states based on triatomic GHZ states 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 ways

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 joint remote preparation of quantum states based on the three-atom GHZ state is based on the interaction between a single two-level atom and a classical electromagnetic field, with the following settings:

(1) Multiple senders at different nodes only know part of the information of the secret quantum state, but not all information; therefore, it is impossible for any sender to disclose the secret information;

(2) Only with the cooperation of multiple senders can the secret quantum state be re-established in a third party. The absence of any party will lead to the failure of the preparation process, further ensuring the security of the secret quantum state;

(3) The channel for quantum information transmission is the GHZ-type entanglement between three atoms, which is relatively easy to prepare experimentally, and the entanglement degree between the three atoms is the largest;

(4) The two senders share information about the secret quantum state, and the way the information is distributed between the two is related to the success of the preparation of the secret quantum state;

(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 technical solution adopted by the present invention involves three spatially separated participants, and two senders (the first sender Alice and the second sender Bob) remotely assist a receiver (the receiver Carol) to recover the secret Single-atom qubit states:

|Φ＞=α|g＞+β|e＞

Where |g> and |e> represent the ground state and excited state of two-level atoms respectively, the parameters α and β are real numbers, and the condition α ² +β ² =1 is satisfied. The parameters α and β describe all the information of the secret qubit, which is 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 GHZ-type quantum entanglement state composed of three two-level atoms:

The first atom 1 represented by the above formula belongs to the first sender Alice, the second atom 2 represented by the above formula belongs to the second sender Bob, and the third atom 3 represented by the above formula 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.

Fig. 1 schematically shows a flow chart of a method for joint remote preparation of quantum states based on triatomic GHZ states according to a preferred embodiment of the present invention. As shown in Figure 1, in order to restore the secret single-qubit state, the specific steps of the three participants are as follows:

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 senders adjust the complex amplitude of the classical electromagnetic field according to their own information about the parameters α and 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:

where θ _i =Ω _i |A _i |t _i .

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 atoms they own respectively, judge that the atoms are 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 possibilities 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 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 state |Φ＞ whether it has been recovered.

If the splitting of parameters α and β conforms to the following relationship:

α ₁ α ₂ =α, β ₁ β ₂ =β.

1. 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 , the receiver Carol can judge the third atom 3 is in a secret single-qubit state.

2. When the classic information from the two senders shows that the first atom 1 and the second atom 2 are in the excited state at the same time, that is, the state of the two atoms is |e> ₁ |e> ₂ , the receiver Carol makes the third atom 3 Through a classical electromagnetic field, adjust the complex amplitude of the classical electromagnetic field The coupling coefficient Ω ₃ between the atom and the classical field, and the flight time t ₃ of the atom in the classical field, make Ω ₃ |A ₃ |t ₃ = π/2, Thereby converting the third atom 3 into a secret single-qubit state.

If the splitting of parameters α and β conforms to the following relationship:

1. 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 , the receiver Carol can judge that the first atom Triatomic 3 is in a secret single-qubit state.

2. When the classic information from the two senders shows that the first atom 1 and the second atom 2 are both in the ground state, that is, the state of the two atoms is |e＞ ₁ |g＞ ₂ , the receiver Carol makes the third atom 3 Through a classical electromagnetic field, adjust the complex amplitude of the classical electromagnetic field The coupling coefficient Ω ₃ between the atom and the classical field, and the flight time t ₃ of the atom in the classical field, make Ω ₃ |A ₃ |t ₃ = π/2, Thereby converting the third atom 3 into a secret single-qubit state.

The present invention has at least the following advantages:

(1) Many related research results in the past only discuss how to achieve remote reconstruction of a quantum state by multiple senders working together from the mathematical level. The difference is that in the specific physical system of two-level atoms and classical light field, the present invention designs a method for joint remote preparation of single-atom states with the participation of three parties. The interaction between atoms and classical fields has been a very mature technology in the laboratory at present, so the method of the present invention 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, the present invention adopts the two-level atom 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, GHZ-type entanglement exhibits stronger uncorrelated properties among three bodies and is easier to prepare experimentally, making it considered an ideal entanglement resource in quantum information processing. The method of the invention adopts the GHZ type entanglement state composed of three atoms as the channel for quantum information transmission, which improves the success probability of the communication process and is more operable in practice.

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 (3)

1. A method for joint remote preparation of quantum state based on three-atom GHZ state is used for enabling a first sender and a second sender to remotely assist a receiver to recover secret single-atom quantum bit state | phi |)>＝α|g>+β|e&gt, wherein | g&gt, and | e > respectively represent the ground state and excited state of two-level atoms, parameters alpha and beta are real numbers, and the condition alpha is satisfied ² +β ² =1; moreover, the parameters α and β describe all the information of the secret qubit; the parameters α and β are split into two parts, each owned by a two-bit sender, so that the information { α } owned by the first sender ₁ ，β ₁ Information { alpha } owned by the second sender ₂ ，β ₂ }; the first sender, the second sender and a receiver share a GHZ type quantum entangled state composed of three atoms with two energy levelsWherein the first atom 1 belongs to a first sender, the second atom 2 belongs to a second sender, and the third atom 3 belongs to a recipient;

the method comprises the following steps:

the first step is as follows: the first sender and the second sender respectively make the atoms owned by the first sender pass through a classical electromagnetic field, and the frequency of the classical electromagnetic field is resonant with the transition frequency between the atomic ground state and the excited state; the sender follows the respective owned information { alpha ] about the parameters alpha and beta _i ，β _i Adjusting the complex amplitude of the classical electromagnetic fieldCoefficient of coupling between atom and classical field omega _i And the time of flight t of an atom in a classical field _i Thereby satisfying the following conditions:

wherein theta is _i ＝Ω _i |A _i |t _i ；

The second step is as follows: after the first step is completed, the quantum state of the system composed of three atoms will evolve into the following form:

at this time, the first sender and the second sender respectively measure the atoms owned by the first sender, judge that the atoms are in a ground state | g > or an excited state | e >, and send the measurement results to the receiver through a classical channel;

the third step: the receiver judges the state of the third atom 3 mastered by the receiver according to the classical information from the two senders and by combining the splitting mode of the parameters alpha and beta, so that whether the secret single quantum bit state | phi > is recovered or not is known;

wherein in the third step, if the split of the parameters α and β are in accordance with the relationship

α ₁ α ₂ ＝α，β ₁ β ₂ = β, the following steps are performed:

when classical information from a first sender and a second sender shows that both the first atom 1 and the second atom 2 are in the ground state, i.e. the state of both atoms is | g > ₁ |g＞ ₂ The receiver judges that the third atom 3 is in a secret single-qubit state;

when classical information from a first sender and a second sender shows that first atom 1 and second atom 2 are simultaneously in excited states, i.e. the states of both atoms are | e > ₁ |e＞ ₂ The receiver passes a third atom 3 through a classical electromagnetic field, the complex amplitude of which is adjustedCoefficient of coupling between atom and classical field omega ₃ And time of flight t of an atom in a classical field ₃ So that Ω is ₃ |A| ₃ t ₃ ＝π/2,Thereby converting the third atom 3 to a secret single-quantum bit state;

alternatively, in the third step, if the split of the parameters α and β complies with the relationship:

the following steps are performed:

when classical information from a first sender and a second sender shows that the first atom 1 is in the ground state and the second atom 2 is in the excited state, i.e. the state of both atoms is | g > ₁ |e＞ ₂ The receiver judges that the third atom 3 is in a secret single-qubit state;

when classical information from two-bit senders shows that both first atom 1 and second atom 2 are in the ground state, i.e. the state of both atoms is | e> ₁ |g> ₂ The recipient passes a third atom 3 through a classical electromagnetic field, the complex amplitude of which is adjustedCoupling coefficient between atom and classical field omega ₃ And the time of flight t of an atom in a classical field ₃ So that Ω is ₃ |A ₃ |t ₃ ＝π/2,Thereby converting the third atom 3 to a secret single-quantum bit state.

2. The method for the joint remote preparation of quantum states based on a triatomic GHZ state of claim 1, wherein a quantum communication channel and a classical communication channel are established between a first sender and a second sender, respectively, and a receiver.

3. The method for the joint, remote preparation of quantum states based on a triatomic GHZ state of claim 1 or 2, wherein there is no communication link between the first sender and the second sender.