CN105471515B - The long-range method for preparing quantum state of joint based on three atom GHZ states - Google Patents
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Abstract
The invention provides a kind of long-range method for preparing quantum state of the joint based on three atom GHZ states.First sender and the monatomic quantum bit state of second sender's remote assistance, one recipient's Restore Secret | Φ ＞=α | g ＞+β | e ＞, wherein | g ＞ and | e ＞ represent the ground state and excitation state of Two level atom respectively, parameter alpha and β are real number, and meet condition α2+β2=1；Moreover, parameter alpha and β describe all information of secret quantum bit；Parameter alpha and β are split as two parts, are possessed respectively by two senders so that the information { α that the first sender possesses1, β1, the information { α that the second sender possesses2, β2}；The GHZ type Quantum Entangled States being made up of three Two level atoms are shared between first sender, the second sender and a recipientWherein the first atom 1 belongs to the first sender, and the second atom 2 belongs to the second sender, and the 3rd atom 3 belongs to recipient.
Description
Technical Field
The invention relates to the field of quantum information and communication networks, in particular to a method for jointly and remotely preparing a quantum state based on a three-atom GHZ state.
Background
Quantum communication is a new communication method emerging in recent years. By encoding information in a physical system with quantum characteristics and utilizing the quantum characteristics of the system state, such as quantum entanglement, measurement collapse, quantum state unclonable and the like, the quantum communication process is safer, more efficient and more interference-resistant than classical communication. With the intensive research on quantum communication networks, various quantum communication methods have been proposed to solve the communication problems such as information transmission, information encryption, key distribution, and secret sharing.
It is assumed that after some information processing, e.g. after one quantum secret sharing, classical information describing the content of one secret qubit is split and distributed to different nodes of the quantum network. That is, each node only grasps a portion of the information of the secret qubit state; none of the nodes possesses the full information of this secret qubit and can independently recover the information of the secret qubit. The problem now is how to be able to reconstruct the secret information at a new node. To this end, methods for the remote preparation of quantum states by multiparty integration have been proposed (see references [1] to [10 ]). The methods respectively utilize different quantum entangled states as transmission channels of quantum information to complete the joint remote preparation task of different types of quantum bit states. However, these studies only propose a method for multi-party joint remote preparation of qubit states from a mathematical level, and do not propose a practical solution for a specific physical system. The experimental scheme proposed by a few researchers (see reference 11] [12 ]) uses a single photon as a carrier of information, and the single photon is easily affected by the environment and annihilated in the actual operation.
At present, few researches on methods for jointly and remotely preparing quantum states are discussed for specific physical systems, how to realize the process in the actual physical world is not considered, and the problem of whether the process is executable or not is not discussed. The physical scheme of the digressive number is mainly discussed in the photonic system. Although the photon transmission speed is high, the decoherence time is short, and the annihilation is easy in the actual physical environment. Moreover, the information carrier does not need to be transmitted in the process of remotely preparing the quantum state, and the information carrier needs to be properly operated. It follows that photonic systems are not ideal physical systems for accomplishing the joint remote preparation of quantum states.
List of references:
[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-qubit state,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,Quantum Inf.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.Process12,2325(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-type states,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 prepa-ration,Quantum Inf.Process 11,751(2012)。
disclosure of Invention
The invention aims to solve the technical problem of providing a method for jointly and remotely preparing a quantum state based on a three-atom GHZ state aiming at the defects in the prior art. The invention provides a method for remotely preparing a secret single quantum bit state by taking two-energy-level atoms as an information carrier, utilizing the interaction between a single two-energy-level atom and a classical electromagnetic field and taking a three-atom GHZ type entangled state as a transmission channel of quantum information, wherein two senders and one receiver participate in the method.
To achieve the above technical object, according to the present invention, there is provided a method for remotely preparing quantum states based on a union of three-atomic GHZ states, for enabling a first sender and a second sender to remotely assist a one-bit receiver to recover a secret single-atomic quantum bit state | Φ > = α | g > + β | e >,wherein | g > and | e > respectively represent the ground state and the excited state of atoms with two energy levels, parameters α and β are real numbers, and the condition α 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 levelsWhere 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.
Preferably, a quantum communication channel and a classical communication channel are established between the first sender and the second sender and the receiver, respectively.
Preferably, there is no communication link between the first sender and the second sender.
Preferably, the method for the remote preparation of quantum states based on the combination of three-atom GHZ states comprises:
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 fieldCoupling coefficient 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 to 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 result to the receiver through a classical channel;
the third step: the receiver judges the state of the third atom 3 grasped by the receiver according to the classical information from the two senders and 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.
Preferably, 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 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;
preferably, 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 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 3 |A 3 |t 3 ＝π/2,Thereby converting the third atom 3 to a secret single-quantum bit state.
Therefore, the invention provides a method which takes two-energy-level atoms as information carriers and can restore secret information after quantum secret sharing. In the method, each sender only grasps one part of secret information, and the secret information is transmitted through a quantum channel, so that the method has good safety. In the method, the technology of controlling the atomic state is realized by utilizing the interaction of the classical electromagnetic field and a single two-energy-level atom, and the method has practical operability; meanwhile, the three-atom GHZ type entangled state is adopted as the quantum channel, so that the communication efficiency can be improved, and the manufacturing is more convenient.
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A more complete understanding of the present invention, and the attendant advantages and features thereof, will be more readily understood by reference to the following detailed description when considered in conjunction with the accompanying drawings wherein:
fig. 1 schematically shows a flow diagram of a method for the joint remote preparation of quantum states based on a three-atom GHZ state, according to a preferred embodiment of the present invention.
It is to be noted, however, that the appended drawings illustrate rather than limit the invention. It is noted that the drawings representing structures may not be drawn to scale. Also, in the drawings, the same or similar elements are denoted by the same or similar reference numerals.
Detailed Description
In order that the present invention may be more clearly and easily understood, the following detailed description is given in conjunction with the specific embodiments and the accompanying drawings.
The method for the joint remote preparation of quantum states based on a three-atomic GHZ state according to a preferred embodiment of the present invention is based on the interaction between a single two-level atom and a classical electromagnetic field, with the following settings:
(1) Senders with multiple bits at different nodes only know part of the information of the secret quantum state, not all information; thus, it is not possible for any one sender to reveal secret information;
(2) Only under the cooperative action of a plurality of senders, the secret quantum state can be re-established in a third party, and the absence of any party can cause the failure of the preparation process, so that the safety of the secret quantum state is further ensured;
(3) The channel for quantum information transmission is GHZ type entanglement among three atoms, is relatively easy to prepare in experiments, and the entanglement degree among the three atoms is maximum;
(4) Two senders share information of the secret quantum state, and the information distribution mode between the two senders is related to the success of secret quantum state preparation;
(5) The state of an atom represents information. By utilizing the interaction between the atoms with two energy levels and the classical electromagnetic field, the manipulation of the atomic state, namely the processing of information can be realized.
The technical scheme adopted by the invention relates to participants separated in a three-dimensional space, and two senders (a first sender Alice and a second sender Bob) remotely assist a receiver (a receiver Carol) to recover a secret single-atom quantum bit state:
|Φ＞＝α|g＞+β|e＞
wherein | g > and | e > represent a ground state and an excited state of a two-level atom, respectively, parameters α and β are real numbers, and a condition α is satisfied 2 +β 2 And =1. The parameters α and β describe all the information of the secret qubit, split into two parts, owned by the two senders. It is not assumed that the first sender Alice has information of { α } 1 ，β 1 The information owned by the second sender Bob is { alpha } 2 ，β 2 }. Two senders and one receiver share a GHZ type quantum entangled state composed of three two-energy level atoms:
wherein the first atom 1 represented by the above formula belongs to a first sender Alice, the second atom 2 represented by the above formula belongs to a second sender Bob, and the third atom 3 represented by the above formula belongs to a receiver Carol. Quantum communication channels and classical communication channels are established between the two senders and the receiver respectively; in order to ensure the security of the secret qubit, the two senders are not in communication with each other.
Fig. 1 schematically shows a flow diagram of a method for the joint remote preparation of quantum states based on a three-atomic GHZ state according to a preferred embodiment of the invention. As shown in fig. 1, to recover the secret single qubit state, the three-bit participants have the following specific steps:
first step S1: the two transmitters each pass their own atoms through a classical electromagnetic field whose frequency should resonate at the transition frequency between the atomic ground and excited states. 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 。
A second step S2: after the first step S1 is completed, the quantum state of the system composed of three atoms will evolve into the following form:
at this time, two senders respectively measure the atoms they own, determine whether 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.
A third step S3: there are four different possibilities for the measurement of the two senders, corresponding to each measurement the third atom 3 will collapse into a different quantum state. The receiver Carol, based on the classical information from both senders and by combining the splitting of the parameters α and β, can determine the state of the third atom 3 she is in, and thus know whether the secret single-quantum bit state | Φ > is recovered.
If the split of the parameters α and β obeys the following relationship:
α 1 α 2 ＝α，β 1 β 2 ＝β。
1. 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 | g > 1 |g＞ 2 The receiver Carol may determine that the third atom 3 is in a secret single qubit state.
2. When classical information from two bit senders shows that first atom 1 and second atom 2 are in excited states at the same time, i.e. the state of both atoms is | e > 1 |e＞ 2 The recipient Carol passes the third atom 3 through a classical electromagnetic field, the complex amplitude of which is regulatedCoupling coefficient between atom and classical field omega 3 And time of flight t of an atom in a classical field 3 So that Ω 3 |A 3 |t 3 ＝π/2,Thereby converting the third atom 3 to a secret single-quantum bit state.
If the split of the parameters α and β obeys the following relationship:
1. when classical information from two bit senders 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 Carol may determine that the third atom 3 is in a secret single qubit state.
2. 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 receiver Carol order the third originThe son 3 passes through a classical electromagnetic field to adjust the complex amplitude of the classical electromagnetic fieldCoupling 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.
The invention has at least the following advantages:
(1) Many related research efforts in the past only discuss, at a mathematical level, how to achieve remote reconstruction of a quantum state by cooperative multiple senders. In contrast, the method for jointly and remotely preparing the monatomic state by three parties is designed in a specific physical system of the two-energy-level atom and the classical optical field. The interaction between atoms and classical fields is a very mature technology in laboratories at present, so that the method has good operability;
(2) The quantum states of atomic systems have longer decoherence times, or are more stable, than photonic systems, and are therefore generally considered ideal fixed bits. Which makes it more suitable than photons for integrated remote fabrication processes. Since the physical system as the information carrier does not need to be transported to another location in the process of preparing the quantum states remotely, but only needs to be operated locally. Therefore, the invention adopts two-energy-level atoms as information carriers;
(3) The current study on three-body entanglement shows that the entanglement among three quantum systems has only two non-equivalent modes, one is GHZ type, and the other is W type. In contrast, GHZ-type entanglement exhibits stronger intertrisomy-noncorrelation properties and is experimentally easier to prepare, making it considered an ideal entanglement resource in quantum information processing. The method of the invention adopts the GHZ type entangled state composed of three atoms as the channel for quantum information transmission, improves the success probability of the communication process and has better operability in practice.
In addition, it should be noted that the terms "first", "second", "third", and the like in the specification are used for distinguishing various components, elements, steps, and the like in the specification, and are not used for indicating a logical relationship or a sequential relationship between the various components, elements, steps, and the like, unless otherwise specified or indicated.
It is to be understood that while the present invention has been described in conjunction with the preferred embodiments thereof, it is not intended to limit the invention to those embodiments. It will be apparent to those skilled in the art that many changes and modifications can be made, or equivalents employed, to the presently disclosed embodiments without departing from the intended scope of the invention. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention are still within the scope of the protection of the technical solution of the present invention, unless the contents of the technical solution of the present invention are departed.
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>, wherein | g>, 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.
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| CN103618695A (en) * | 2013-11-07 | 2014-03-05 | 南京信息工程大学 | Total probability arbitrary multiparty JRSP method |
| CN104601248A (en) * | 2014-12-23 | 2015-05-06 | 上海电机学院 | Multi-party combined remote quantum state preparation method based on single atom operations |
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| CN103618695A (en) * | 2013-11-07 | 2014-03-05 | 南京信息工程大学 | Total probability arbitrary multiparty JRSP method |
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