CN110808831B - Combined remote state preparation method based on seven-bit quantum channel - Google Patents
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Abstract
The invention discloses a combined remote state preparation method based on a seven-bit quantum channel. The invention relates to a combined remote state preparation method based on a seven-bit quantum channel, which comprises the following steps: under the control of Duke, Alice, Bob and Charlie are both a sender and a receiver, and the two are combined to prepare the required target state; the whole method consists of Alice, Bob, Charlie, Duke and a seven-bit quantum channel, wherein Alice, Bob and Charlie are a sender and a receiver, and Duke is a controller; under control of Duke, Alice and Bob combine to form the Charlie prepared target state, Bob and Charlie combine to form Alice prepared target state, and Charlie and Alice combine to form Bob prepared target state. The invention has the beneficial effects that: 1. in the invention, Alice, Bob and Charlie are both a sender and a receiver, and any two of the Alice, the Bob and the Charlie are used for preparing the target state for the third party, thereby greatly improving the state preparation efficiency. 2. According to the invention, 3 target states can be prepared simultaneously, and the preparation speed of a plurality of target states is improved.
Description
Technical Field
The invention relates to the field of quantum state preparation, in particular to a combined remote state preparation method based on a seven-bit quantum channel.
Background
Quantum communication is an important branch of quantum informatics, and is an earlier field of research in quantum information. Quantum communication is the efficient transfer of information in quantum states as units of information. In quantum communication, besides the traditional classical channel, a quantum channel between communication parties needs to be established more mainly. What is called a quantum channel is in fact a quantum entanglement between communicating parties. The application of quantum entanglement in communication creates an incredible miracle of classical information theory, such as 'quantum dense coding' for transmitting classical bits by using a quantum channel, 'quantum invisible state' for transmitting quantum states by using a classical auxiliary method, and 'absolute safe quantum cryptography' required by information security transmission [1 ].
The quantum entanglement state is the quantum state which most commonly exists in a quantum mechanics multi-particle system or a multi-degree-of-freedom system but is very special. It is one of the wonderful characteristics of quantum mechanics, namely that the measurement result of one subsystem cannot be independent of the measurement parameters of other subsystems. In 1935 Einstein, Podolsky, Rosen published a short and very important article [2] first related to entanglement states, later called the paradox EPR. Schrodinger in the same year defined the concept of entanglement status in his famous article [3 ]. The proposal of entangled state prompts people to deeply discuss the traditional quantum mechanics, and the theory and oath related to entangled state are the main direction of the quantum mechanics development in recent decades. The entangled state plays an important role in understanding the basic concept of quantum mechanics. But the function of the quantum information is not only the same, and with the vigorous development of a new field of quantum information science, the quantum entanglement state gradually ascends the stage of the quantum information field and establishes the dominant position of the quantum information field. The quantum entangled state is used as a carrier of quantum communication and quantum computation, and is widely applied to the fields of quantum invisible state transfer, quantum key distribution, quantum dense coding, quantum computation and the like.
Remote preparation of quantum states (remote state preparation) is the successful realization of the transfer of a known quantum state based on classical information and entangled states. RSP is used to transfer a known state between sender Alice and receiver Bob. Bob obtains the target state by performing an appropriate single operation. In 2000, Lo 4, Pati 5 and Bennett 6 et al proposed schemes for the remote preparation of known quantum states. Stealth transmission schemes and remote fabrication schemes have many similarities, but the information of the quantum states to be transmitted in the former is unknown, which is quite different from the latter. In the remote state preparation scheme, it is a prerequisite that the sender knows the information of the quantum state to be transmitted, and is therefore also referred to as "quantum invisible transmission of a known state". Basic idea of remote state preparation: first, sender Alice and receiver Bob share the entangled resource, and Alice performs some classical information and local operations to achieve the transmission of a quantum state that is completely known to her but unknown to Bob. Seven-bit quantum channels are also commonly used for quantum transport. For example, Yang et al proposed an improved quantum proxy blind signature scheme based on controlled stealth states [7 ]. Lie sensitivity proposes an improved quantum stealth state scheme for a five-qubit unknown state with seven-qubit quantum channels [8 ]. Remote state preparation is an emerging subject, draws attention of various national scholars from the beginning, and makes great progress on theory and experiments nowadays. In theory, many schemes have been proposed. To date, RSP has gained increasing interest due to the lower consumption of qubit resources. Various RSP protocols have been proposed, such as deterministic RSP [9], federated RSP (JRSP) [10,11], Controlled RSP (CRSP) [12] - [17], forgetful RSP [18], low-entanglement RSP [19] and continuous variable RSP [20 ].
There are many current approaches to JRSP. In JRSP, several senders share knowledge of the readiness state. Each sender holds part of the information, the receiver has no information about the status. When all senders collaborate, the receiver can reconstruct the desired state by some manipulation of his own particles. For example, in 2015, Li proposed a JRSP [21] for a two-qubit equatorial state. 2016, King et al. A DJRSP scheme is proposed in which four qubit states are prepared as quantum channels through two GHZ states [22 ]. 2017, Fu et al. This idea is extended to implement the JRSP scheme of any four-qubit W-type entangled states by using two three-qubit GHZ states as quantum channels [23 ]. In 2017, Wang proposed bi-directional control joint remote status preparation by seven qubit entangled state [24 ]. In 2018, Xiao et al. A JRSP scheme is proposed in which single-quantum-site states are prepared by three-atom entangled GHZ-type states [25 ]. 2018, Liao et al. A JRSP scheme for any two-qubit state is proposed by cluster states [26 ].
Reference documents:
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[2]Einstein A,PodolskyB,Rosen N.Can Description of Physical Reality be Considered Complete?[J].Phys.Rev.,1935,47:777—780.
[3]Schrodinger E.Die Gegenwartige Situation in derQuantenmechanik[J].NaturwissenSchaften,1935,23:807~812;823—828:844—849.
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[6]J.-F.Li,J.-M.Liu,X.-L.Feng,and C.H.Oh,“Deterministic remote two-qubit state preparation in dissipative environments,”Quantum Inf.Process.,vol.15,no.5,pp.2155-2168,2016.
[7]Yang Y Y,Xie S C,Zhang J Z.An Improved Quantum Proxy Blind Signature Scheme Based on Genuine Seven-Qubit Entangled State[J].International Journal of Theoretical Physics,2017,56(7):2293-2302.
[8]Yang Y,Jiang M,Zhou L L.Improving the Teleportation Scheme of Five-Qubit State with a Seven-Qubit Quantum Channel[J].International Journal of Theoretical Physics,2018,57(11):3485-3491.
[9]B.An Nguyen,T.B.Cao,V.Don Nung,and J.Kim,“Remote state preparation with unit success probability,”Adv.Natural Sci.,Nanosci.Nanotechnol.,vol.2,p.035009,Jul.2011.
[10]Choudhury B S,Dhara A.Joint remote state preparation for two-qubit equatorial states.[J].Quantum Information Processing,2015,14(1):373-379.[11]Nguyen B A 2010 Opt.Commun.2834113-17
[11]Zhang C Y,Bai M Q,Zhou S Q.Cyclic joint remote state preparation in noisy environment[J].Quantum Information Processing,2018,17(6):146.
[12]L.Huang and H.-X.Zhao,“Controlled remote state preparation of an arbitrary two-qubit state by using GHZ states,”Int.J.Theor.Phys.,vol.56,no.3,pp.678-682,2017.
[13]Chen X B,Ma S Y,Su Y,et al.Controlled remote state preparation of arbitrary two and three qubit states via the Brown state[J].Quantum Information Processing,2012,11(6):1653-1667.
[14]Kiktenko E O,Popov A A,Fedorov A K.Bidirectional imperfect quantum teleportation with a single Bell state[J].Physical Review A,2016,93(6):062305.
[15]Da Z,Zha X W,Duan Y J,et al.Deterministic Controlled Bidirectional Remote State Preparation Via a Six-qubit Maximally Entangled State[J].International Journal of Theoretical Physics,2016,55(1):440-446.
[16]Da Z,Zha X W,Duan Y J,et al.Deterministic Controlled Bidirectional Remote State Preparation Via a Six-qubit Maximally Entangled State[J].International Journal of Theoretical Physics,2016,55(1):440-446.
[17]Chen X B,Sun Y R,Xu G,et al.Controlled bidirectional remote preparation of three-qubit state[J].Quantum Information Processing,2017,16(10):244.
[18]Leung,D.W.,Show,P.W,“Oblivious remote state preparation,”Phys.Rev.Lett.,90,127905,2003.
[19]DevetakI,Berger T.Low-entanglement remote state preparation.[J].Physical Review Letters,2001,87(19):197901.
[20]Paris,M.G.A,Cola,M.,Bonifacio,R,“Remote state preparation and teleportation in phase space”J.Opt.B.5(3),247-50,2003.
[21]X.Li,S.Ghose,“Optimal joint remote state preparation of equatorial states,”Quantum Information Processing,14(12):4585-4592,2015.
[22]Wang H B,Zhou X Y and An X X,2016 International Journal of Theoretical Physics 55 3588-96
[23]Fu H,Ma P C,Chen G B,et al.Efficient schemes for deterministic joint remote preparation of an arbitrary four-qubit W-type entangled state[J].Pramana,2017,88(6):92.
[24]X.Y.Wang,Z.W.Mo,“Bidirectional Controlled Joint Remote State Preparation via a Seven-Qubit Entangled State,”International Journal of Theoretical Physics,56(4):1052-1058,2017.
[25]Xiao X Q,Yao F,Lin X,et al.Joint Remote State Preparation of a Single-Atom Qubit State via a GHZ Entangled State[J].International Journal of Theoretical Physics,2018,57(4):1132-1140.
[26]Liao Y M,Zhou P,Qin X C,et al.Efficient joint remote preparation of an arbitrary two-qubit state via cluster and cluster-type states[J].Quantum Information Processing,2014,13(3):615-627.
Disclosure of Invention
The invention aims to provide a combined remote state preparation method based on a seven-bit quantum channel.
In order to solve the technical problem, the invention provides a combined remote state preparation method based on a seven-bit quantum channel, which comprises the following steps: under the control of Duke, Alice, Bob and Charlie are both a sender and a receiver, and the two are combined to prepare the required target state; the whole method consists of Alice, Bob, Charlie, Duke and a seven-bit quantum channel, wherein Alice, Bob and Charlie are a sender and a receiver, and Duke is a controller; under the control of Duke, Alice and Bob are combined to be a Charlie preparation target state, Bob and Charlie are combined to be an Alice preparation target state, and Charlie and Alice are combined to be a Bob preparation target state; the method comprises the following steps:
step 1: the target state and channel are as follows:
alice and Charlie want to prepare Bob with an arbitrary quantum state, in the form:
wherein α and β are amplitude coefficients and satisfy | α! α -2+|β|2=1,0≤θ1<2π。
Alice and Bob want to prepare Charlie with an arbitrary quantum state, in the form:
wherein γ and δ are amplitude coefficients and satisfy | γ tint2+|δ|2=1,0≤θ2<2π。
If Bob and Charlie want to prepare an arbitrary quantum state for Alice, the form is as follows:
wherein m and n are amplitude coefficients and satisfy | m2+|n|2=1,0≤θ3<2π。
The expression of Alice, Bob, Charlie, Duke sharing a seven-bit quantum channel is as follows:
alice has a particle A, A1Bob possesses particles B, B1Charlie possesses particles C, C1Duke possesses particle d.
Respectively introducing auxiliary particles |0 into Alice, Bob and Charlie>A',|0>B',|0>C'And performing a CNOT operation on the particle pairs (a, a '), (B, B ') and (C, C '), and the system expression is as follows:
step 2: amplitude and phase measurements were performed as follows:
alice, Bob, Charlie send A ', B ', C ' to Charlie, Alice, Bob, respectively, and Alice, Bob, Charlie, respectively, for particle A1,B1,C1Performing amplitude measurements, Charlie, Alice, Bob, on the particles a ', B', C;
and step 3: controlling measurement and preparation of target states
For Duke, only after they allow Alice, Bob and Charlie to communicate, they can jointly prepare the target state, so that control party Duke performs a single bit measurement if it needs to prepare it, based on { |% { (X) }j>;j∈{0,1}}
The final system can thus be written as:
alice, Bob and Charlie each have 8 measurement result combinations, and perform a corresponding unitary operation according to the measurement results (I ═ 0)><0|+|1><1|,σx=|0><1|+|1><0|,σz=|0><0|-|1><1| or σy=i(|0><1|-|1><0|)) to obtain the target state.
In one embodiment, in step 2, taking Alice as an example, the following details are provided:
alice first selects a set of orthogonal measurement basis { | mui>;i∈{0,1}}:
|μ0>=α|0>+β|1>,
|μ1>=β|0>-α|1>.
Alice passes through the pair of particles A1Making an amplitude measurement if the measurement is | mu0>Then a measurement base is selected
Bob selects the amplitude measurement basis as follows:
|μ0>′=γ|0>+δ|1>,
|μ1>′=δ|0>-γ|1>.
bob by pairing particles B1Making an amplitude measurement if the measurement is | mu0>', a measurement basis is selected
The amplitude measurement basis selected by Charlie is:
|μ0>″=m|0>+n|1>,
|μ1>″=n|0>-m|1>.
charlie by pairing particles C1Making an amplitude measurement if the measurement is | mu0>", a measurement base is selected
In one embodiment, "Alice, Bob, Charlie each have 8 measurement result combinations, and perform a corresponding unitary operation according to the measurement results (I ═ 0)><0|+|1><1|,σx=|0><1|+|1><0|,σz=|0><0|-|1><1| or σy=i(|0><1|-|1><0|)) to obtain the target state "
The specific operation is as follows:
in one embodiment, the quantum states prepared by Bob of Alice and Charlie are used as an example, if Duke's measurement is | χ0>The measurement result of Alice is | μ1>The measurement result of Charlie isFrom the above table it can be seen that the receiver Bob needs to performThe operation achieves the goal.
In one embodiment, Alice passes through particle A1The measurement of the amplitude is carried out,
In one embodiment, Bob is controlled by controlling particle B1The measurement of the amplitude is carried out,
In one embodiment, Charlie is performed by aligning particles C1The measurement of the amplitude is carried out,
The invention has the beneficial effects that:
1. in the invention, Alice, Bob and Charlie are both a sender and a receiver, and any two of the Alice, the Bob and the Charlie are used for preparing the target state for the third party, thereby greatly improving the state preparation efficiency.
2. According to the invention, 3 target states can be prepared simultaneously, and the preparation speed of a plurality of target states is improved.
3. The three-party combined remote state preparation of the seven-bit quantum can realize amplitude measurement and phase measurement, classical communication and local operation required in the preparation, and has high preparation efficiency.
Drawings
FIG. 1 is a flow chart of the method for the joint remote state preparation based on seven-bit quantum channels according to the present invention.
Fig. 2 is a schematic diagram of a quantum channel of Alice, Bob, Charlie in the seven-bit quantum channel-based joint remote state preparation method of the present invention.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
The technical terms of the invention explain:
1. pauli array
Some unitary matrices, also known as Pauli matrices, are also used in the present invention. The specific form is as follows:
2. CNOT operations
The CNOT operation is a not gate operation, and the two qubits are a control bit and a target bit, respectively. When the control bit is |0>, the target bit is unchanged; when the control bit is |1>, the target bit is inverted. The matrix form that the CNOT operation acts on the qubit pairs is as follows:
referring to fig. 1 and 2, under the control of the controller Duke, Alice, Bob, Charlie combines two by two through seven-bit quantum channels to prepare a target state for a third party, including the following steps: under the control of Duke, Alice, Bob, Charlie are both the sender and the receiver, and the two are combined to prepare the required target state. The whole method consists of Alice, Bob, Charlie, Duke and a seven-bit quantum channel, wherein Alice, Bob and Charlie are a sender and a receiver, and Duke is a controller. Under control of Duke, Alice and Bob combine to form the Charlie prepared target state, Bob and Charlie combine to form Alice prepared target state, and Charlie and Alice combine to form Bob prepared target state. Therefore, the preparation efficiency can be greatly improved, and the complete process comprises the following steps:
step 1: the target state and channel are as follows:
alice and Charlie want to prepare Bob with an arbitrary quantum state, in the form:
wherein α and β are amplitude coefficients and satisfy | α! α -2+|β|2=1,0≤θ1<2π。
Alice and Bob want to prepare Charlie with an arbitrary quantum state, in the form:
wherein γ and δ are amplitude coefficients and satisfy | γ tint2+|δ|2=1,0≤θ2<2π。
If Bob and Charlie want to prepare an arbitrary quantum state for Alice, the form is as follows:
wherein m and n are amplitude coefficients and satisfy | m2+|n|2=1,0≤θ3<2π。
The expression of Alice, Bob, Charlie, Duke sharing a seven-bit quantum channel is as follows:
alice has a particle A, A1Bob possesses particles B, B1Charlie possesses particles C, C1Duke possesses particle d.
Respectively introducing auxiliary particles |0 into Alice, Bob and Charlie>A',|0>B',|0>C'And performing a CNOT operation on the particle pairs (a, a '), (B, B ') and (C, C '), and the system expression is as follows:
step 2: amplitude and phase measurements were performed as follows:
alice, Bob, Charlie send A ', B ', C ' to Charlie, Alice, Bob, respectively, and Alice, Bob, Charlie, respectively, for particle A1,B1,C1An amplitude measurement is performed, Charlie, Alice, Bob, on the particles a ', B', C. Taking Alice as an example, the details are as follows:
alice first selects a set of orthogonal measurement basis { | mui>;i∈{0,1}}:
|μ0>=α|0>+β|1>,
|μ1>=β|0>-α|1>.
Alice passes through the pair of particles A1Making an amplitude measurement if the measurement is | mu0>Then a measurement base is selected
Bob selects the amplitude measurement basis as follows:
|μ0>′=γ|0>+δ|1>,
|μ1>′=δ|0>-γ|1>.
bob by pairing particles B1Making an amplitude measurement if the measurement is | mu0>', a measurement basis is selected
The amplitude measurement basis selected by Charlie is:
|μ0>″=m|0>+n|1>,
|μ1〉″=n|0>-m|1>.
charlie by pairing particles C1Making an amplitude measurement if the measurement is | mu0>", a measurement base is selected
And step 3: controlling measurement and preparation of target states
For Duke, only after they allow Alice, Bob and Charlie to communicate, they can jointly prepare the target state, so that the controller Duke needs to perform a single bit measurement if preparing this patent, and the measurement basis is { | × χj>;j∈{0,1}}
The final system can thus be written as:
alice, Bob and Charlie each have 8 measurement result combinations, and perform a corresponding unitary operation according to the measurement results (I ═ 0)><0|+|1〉〈1|,σx=|0><1|+|1〉〈0|,σz0 to 1 or σy=i(|0〉〈1|-|1><0|)) to obtain a target state, and the specific operation is as follows:
to illustrate the quantum state preparation by Bob of Alice and Charlie, let Duke be the measurement of | χ0>The measurement result of Alice is | μ1>The measurement result of Charlie isFrom the above table it can be seen that the receiver Bob needs to performThe operation achieves the target state.
The first embodiment is as follows: alice and Charlie combined for Bob preparationCombined preparation of Charlie for Alice and BobPreparation of Alice by combination of Bob and CharlieThe complete process comprises the following steps:
step 1: the target state and channel are as follows:
alice and Charlie want to prepare Bob a quantum state, in the form:
alice and Bob want to prepare Charlie with a quantum state in the form:
bob and Charlie want to prepare Alice a quantum state in the form:
the expression of the seven-bit quantum channel shared by Alice, Bob, Charlie and Duke is as follows:
alice has a particle A, A1Bob possesses particles B, B1Charlie possesses particles C, C1Duke possesses particle d.
Respectively introducing auxiliary particles |0 into Alice, Bob and Charlie>A',|0>B',|0>C'And for particle pairs (A, A '), (B, B ') and (C, C ')Line CNOT operation, and thus the system expression is as follows:
step 2: amplitude and phase measurements were performed as follows:
alice, Bob, Charlie send A ', B ', C ' to Charlie, Alice, Bob, respectively, and Alice, Bob, Charlie, respectively, for particle A1,B1,C1An amplitude measurement is performed, Charlie, Alice, Bob, on the particles a ', B', C. The amplitude measurement basis for Alice is as follows:
alice passes through the pair of particles A1Making an amplitude measurement if the measurement is | mu0>Then a measurement base is selected
Bob's amplitude measurement is based on:
bob by pairing particles B1Making an amplitude measurement if the measurement is | mu0>', a measurement basis is selected
The amplitude measurement of Charlie is based on:
charlie by pairing particles C1Making an amplitude measurement if the measurement is | mu0>", a measurement base is selected
And step 3: controlling measurement and preparation of target states
For Duke, only after they allow Alice, Bob, Charlie to communicate, they can jointly prepare the target state, so controller Duke performs a single bit measurement based on { |% χj>;j∈{0,1}}
The whole system thus becomes the following:
alice, Bob and Charlie have 8 kinds of measurement results respectively, and corresponding unitary operation is executed according to the measurement results to obtain a target state, and the specific operation is as follows:
when Duke's measurement is | χ0>dWhen Alice and Charlie are prepared for Bob, if Alice's measurement result isThe measurement result of Charlie isBob only needs to executeThe target state can be obtained by the operation. When Bob and Alice are prepared for Charlie, if Bob's measurement result isThe measurement result of Alice isCharlie needs to executeThe operation achieves the target state. If Charlie and Bob were prepared for Alice, the measurement of Charlie would beBob measures thatAlice needs to executeThe operation achieves the target state.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (1)
1. A combined remote state preparation method based on a seven-bit quantum channel is characterized by comprising the following steps: under the control of Duke, Alice, Bob and Charlie are both a sender and a receiver, and the two are combined to prepare the required target state; the whole method consists of Alice, Bob, Charlie, Duke and a seven-bit quantum channel, wherein Alice, Bob and Charlie are a sender and a receiver, and Duke is a controller; under the control of Duke, Alice and Bob are combined to be a Charlie preparation target state, Bob and Charlie are combined to be an Alice preparation target state, and Charlie and Alice are combined to be a Bob preparation target state; the method comprises the following steps:
step 1: the target state and channel are as follows:
alice and Charlie want to prepare Bob with an arbitrary quantum state, in the form:
wherein α and β are amplitude coefficients and satisfy | α! α -2+|β|2=1,0≤θ1<2π;
Alice and Bob want to prepare Charlie with an arbitrary quantum state, in the form:
wherein γ and δ are amplitude coefficients and satisfy | γ tint2+|δ|2=1,0≤θ2<2π;
If Bob and Charlie want to prepare an arbitrary quantum state for Alice, the form is as follows:
wherein m and n are amplitude coefficients and satisfy | m2+|n|2=1,0≤θ3<2π;
The expression of Alice, Bob, Charlie, Duke sharing a seven-bit quantum channel is as follows:
alice has a particle A, A1Bob possesses particles B, B1Charlie possesses particles C, C1Duke possesses particle d;
respectively introducing auxiliary particles |0 into Alice, Bob and Charlie>A',|0>B',|0>C'And performing a CNOT operation on the particle pairs (a, a '), (B, B ') and (C, C '), and the system expression is as follows:
step 2: amplitude and phase measurements were performed as follows:
alice, Bob, Charlie send A ', B ', C ' to Charlie, Alice, Bob, respectively, and Alice, Bob, Charlie, respectively, for particle A1,B1,C1Performing amplitude measurements, Charlie, Alice, Bob, on the particles a ', B', C;
and step 3: control of measurement and preparation of target states:
for Duke, only after they allow Alice, Bob and Charlie to communicate, they can jointly prepare the target state, so that control party Duke performs a single bit measurement if it needs to prepare it, based on { |% { (X) }j>;j∈{0,1}}
The final system can thus be written as:
alice, Bob and Charlie have 8 measurement result combinations respectively, and corresponding unitary operation is executed according to the measurement results, namely I ═ 0><0|+|1><1|,σx=|0><1|+|1><0|,σz=|0><0|-|1><1| or σy=i(|0><1|-|1><0|), obtaining a target state;
in step 2, taking Alice as an example, the following details are provided:
alice first selects a set of orthogonal measurement basis { | mui>;i∈{0,1}}:
|μ0>=α|0>+β|1>,
|μ1>=β|0>-α|1>;
Alice passes through the pair of particles A1Making an amplitude measurement if the measurement is | mu0>Then a measurement base is selected
Bob selects the amplitude measurement basis as follows:
|μ0>′=γ|0>+δ|1>,
|μ1>′=δ|0>-γ|1>;
bob by pairing particles B1Making an amplitude measurement if the measurement is | mu0>', a measurement basis is selected
The amplitude measurement basis selected by Charlie is:
|μ0>″=m|0>+n|1>,
|μ1>″=n|0>-m|1>;
charlie by pairing particles C1Making an amplitude measurement if the measurement is | mu0>", a measurement base is selected
Each of Alice, Bob and Charlie has 8 measurement result combinations, and executes corresponding unitary operation according to the measurement results, I is ═ 0><0|+|1><1|,σx=|0><1|+|1><0|,σz=|0><0|-|1><1| or σy=i(|0><1|-|1><0|), to obtain the target state "
The specific operation is as follows:
to illustrate the quantum state preparation by using Alice and Charlie as Bob, if Duke's measurement result is | χ%0>The measurement result of Alice is | μ1>The measurement result of Charlie is | τ1 ->From the above table it can be known that the receiver Bob needs to performOperating to obtain a target;
alice passes through the pair of particles A1The measurement of the amplitude is carried out,
Bob by pairing particles B1The measurement of the amplitude is carried out,
Charlie by pairing particles C1The measurement of the amplitude is carried out,
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CN111510289B (en) * | 2020-04-14 | 2021-12-03 | 苏州大学 | Bidirectional single-bit state preparation method based on Brown state and network coding |
CN111555876B (en) * | 2020-05-15 | 2021-08-31 | 苏州大学 | Combined cycle remote state preparation method based on non-maximum entangled channel N-party control |
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