CN109286446A - The method of joint six bit Cluster States of long-range preparation based on GHZ state - Google Patents
The method of joint six bit Cluster States of long-range preparation based on GHZ state Download PDFInfo
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- H04B10/70—Photonic quantum communication
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
- H04B10/50—Transmitters
- H04B10/516—Details of coding or modulation
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Abstract
The present invention relates to the methods of the joint six bit Cluster States of long-range preparation based on GHZ state, one recipient Charlie of two sender Alice and Bob remote assistance prepares six bit Cluster State of target, 2 GHZ channels need to be only shared comprising four step (1) sender Alice first and Bob and recipient Charlie, sender Alice according to the amplitude information of Cluster State, pre-processes quantum communications channel first；(2) sender Alice and Bob measure base according to the fractional phase information structuring of Cluster State to be prepared is corresponding, measure to the particle that it possesses, and measurement result is sent to recipient Charlie；(3) for recipient Charlie according to the measurement result of sender Alice and Bob, the particle in opponent carries out positive operation, obtains intermediate quantum state corresponding with target Cluster State；(4) Charlie introduces auxiliary particle, and executes corresponding operation, restores six bit Cluster State of target.Every sender only grasps the information of a part in the present invention, efficiently avoids the leakage of information, has preferable safety.
Description
Technical field
The present invention relates to quantum communications, more particularly to the side of the joint six bit Cluster States of long-range preparation based on GHZ state
Method.
Background technique
Since C.H.Bennett [1] proposition this concept of quantum teleportation in 1993, quantum information field is obtained
Greatly development, many new concepts, which are put forward one after another, to be come, such as controllable quantum teleportation [2], quantum telecloning [3-
4], quantum dense coding [5-6], quanta identity authentication [7-8].The .2001 such as Quantum Secure Direct Communication, C.H.Bennett
Quantum state is had also been proposed Deng [9] and remotely prepares this new concept, although this preparation process has still used classical channel and quantum logical
Road realizes, but it does not need the state of transmission particle and by operation the multiple particles of distant place can be allowed to tangle, and false
If sender (Al ice) has known state to be prepared in advance, and recipient (Bob) is not aware that, passes in this way with Quantum Teleportation
State is compared, and quantum state is remotely prepared saves on many resources in the process.This concept has attracted the concern of numerous people, and phase
After proposing single-particle state [10-11], 2 Entangleds [12-14], 3 Entangleds [15], 4 particle Cluster States [16-17]
Journey preparation method.
Since Cluster State has stronger stability and anti-interference, Cluster State was put forward for the first time in 2001 from Briegel
Since, just it is widely used in quantum communications.At present, physicists expand extensively Cluster State theoretical and experimental
It studies generally, and achieves significant achievement.Document [18] is successfully realized the preparation of four photon Cluster States, and demonstrates one-dimensional
The feasibility of quantum calculation；Document [19] is proposed prepares four bit clusters in Eurytrema coelomatium and ion trap systems
State；Document [20], which is proposed, prepares Cluster State etc. using the superconductive system of Josephson effect.The long-range preparation of many Cluster States
Scheme is also put forward one after another.2013, document [21] proposed joint four bit Cluster State schemes of long-range preparation.The program is only used
Then dibit nonmaximally entangled state is generalized to multilateral accord as quantum channel.
Bibliography of the present invention is as follows:
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quantum state via dual classical and Einstein-Podolsky-Rosen channels[J]
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Entanglement [J] .Phys Rev A, 1998,58:4394-4400.
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2005.77 (4): 1225-1256.
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[6]Hao Jiucang,Li Chuanfeng,Guo Guangcan.Controlled dense coding
Using the Greenberger-Horne-Zeilinger state [J] .Phys Rev A, 2001,63:54301-
54303.
[7] Zhou Nanrun, Zenng Guihua, Zeng Wenjie, et a1.Cross-center quantum
identification scheme based on teleportation and entanglement swapping[J].Opt
Commun, 2005,254:380.388.
[8]Li Yuanhua,Liu Junchang,Nie Yiyou.Quantum identification scheme of
cross-center based on four-particle cluster slale[J].Chinese Journal of
Quantum Electronics, 2011,28 (1): 52-57.
[9] Bennett C H, Divincenzo D P, Shor P w, et a1.Remote state preparation
[J] .Physical Review Letters, 2001,87 (7): 77902.
[10] Ye Ming, Zhang Yongsheng, Guo Guangcan.Faithful remote state
perparation using finite classical bits and a non-maximally entangled state
[J] .Physical Review A, 2004,69 (2): 716-719.
[11] Babichey S A, Brezger B, Lvovsky A I.Remote preparation of a
single-mode photonic qubit by measuring field quadrature noise[J].Physical
Re, review letters, 2004,92 (4): 47903.
[12]Xiao Xiaoqi,_Liu Jinming._Remote preparation of a tow-particle
entangled state via tow tripartite W entangled states[J].International
Journal of Theoretical Physics, 2007,46 (10): 2378-2383.
[13] Hou Kui, Wang Jing, Yuan Hao, et a1.Multiparty-controlled remote
Preparation of tow-partical state [J] .Communications in Theoretical Physics,
2009,52 (5): 848-852.
[14] Wang D, Zha X W, _ Lan Q.Joint remote state preparation of arbitrary
Tow-qubit state with six-qubit state [J] .Optics Communications, 2011,284 (24):
5853-5855.
[15] Liu Honghui, Cheng Liuyong, Shao xiaoqiang, et a1.Joint remote state
preparation of arbitrary tow-and three-particlestates[J].International Jornal
Of Theoretical Physics, 2011,50 (10): 3023-3032.
[16]Ma Pencheng,Zhan YOubang.Scheme for remotely preparing a four-
Particle entangled cluster-type state [J] .Optics communications, 2010,283 (12):
2640-2643.
[17]Ma Songya,Chen xiubo,Luo Mingxing,et al.Remote preparation of a
Four-particle cluster-like entangIed [J] .optics Communication, 2011,284 (16):
4088-4093.
[18]Zou X B,Mathis W.Generating a four-photon polarizationentangled
cluster state[J].Physical Review A,2005,71(3):309-315.
[19]Zheng X J,Xu H,Fang Maofa,et al.Preparation of the four-qubit
cluster states in cavity QED and the trapped-ion system[J].Chinese Physics B,
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[20]YoKoYama S,UKAI R,RMSTRONG S C,et al.Opt ical generation of
ultra-large-scale continuous-variable cluster states[J].International Nano-
optoelectronics Workshop,2013,78(1):225–226
[21]HOU K.Joint remote preparation of four-qubit cluster-type states
with multiparty[J].Quantum Information Processing,2013,12(12):3821–3833
Summary of the invention
Based on this, it is necessary in view of the above technical problems, provide a kind of joint based on GHZ state and remotely prepare six bit groups
The method of cluster state realizes efficiently six bit Cluster States of the long-range preparation of joint.
A method of the joint six bit Cluster States of long-range preparation based on GHZ state, comprising:
Two sender's remote assistances, one recipient prepares the form of six bit Cluster State of target are as follows:
Wherein, coefficient a0,a1,a2,a3For plural and they meet normalizing condition, phase theta1,θ2,θ3[0,2 π) it
Between.Alice knows the amplitude information a of Cluster State to be prepared0,a1,a2,a3With a part of phase informationBob
Know another part phase information of state to be prepared
Charlie does not know about state to be prepared.
Sender Alice, Bob and recipient Charlie share 2 GHZ Quantum Entangled States:
Wherein Alice possesses particle A1,A2, Bob possesses particle B1,B2, Charlie possesses particle C1,C2。
The first step, amplitude modulation, Alice introduce auxiliary particle | 0 >a, and the particle A that oneself is possessed1、A2With it is auxiliary
Particle a is helped to execute positive operationPositive operationConcrete form is as follows:
Wherein
Entire quantized system at this time are as follows:
Then Alice executes single-particle measurement to auxiliary particle a, if measurement result is | 0 >aSo whole system is collapsed
Are as follows:
Otherwise, preparation failure
Second step, phase-modulation, Alice fractional phase information structuring measure base to particle A accordingly1A2Projection is executed to survey
Amount, measurement base are as follows:
Bob constructs corresponding measurement base to particle B according to another part phase information simultaneously1B2Execute projection measurement, measurement
Base is as follows:
Based on above two groups of measurement bases, entire quantized system are as follows:
There are four types of possible for the measurement result of Alice:Corresponding four kinds are not
Same encoded information 00,01,10,11.Also there are four types of may respectively be the measurement result of Bob simultaneously:Corresponding four kinds of encoded informations 00,01,10,11, when Alice and Bob is completed
After measurement, measurement result is sent to by recipient Charlie by classical channel.Specifically, if the measurement result of Alice isPair answer encoded information 00, the measurement result of Bob isCorresponding encoded information is that 01, Alice and Bob will be surveyed
Amount result is corresponding to be passed through classical channel at classical information and is sent to recipient Charlie, then Alice that Charlie is received and
The classical information that Bob is sent is 00 and 01, at this time the particle C in Charlie hand1、C2State then become
Third step, according to the measurement result of Alice and Bob, Charlie executes corresponding positive operation
Obtain the dibit quantum state closely related with six bit Cluster States to be prepared:
Specifically, according to the measurement result of Alice and Bob, the particle that Charlie possesses it is executedOperation:Restore intermediate quantum state corresponding with target Cluster State.WhenSoThat is Charlie is to particle C1I operation is executed, whenSoI.e.
Charlie is to particle C1Execute Z operation.It is similar therewith, whenSoI.e. Charlie is to particle
C2I operation is executed, whenSoThat is Charlie is to particle C2Execute Z operation.
4th step, Charlie introduce auxiliary particle, and execute corresponding replacement operator, restore six bit Cluster State of target.
Specifically, Charlie is firstly introduced into four auxiliary particlesWhole system can be rewritten into:
Then Charlie is to particle to C2And C4(C2To control quantum bit, C4For target quantum bit), C4And C6(C4
To control quantum bit, C6For target quantum bit) CNOT operation is successively executed, while to particle to C1And C3(C1For control amount
Sub- bit, C3For target quantum bit), C3And C5(C3To control quantum bit, C5For target quantum bit) successively execute CNOT
Operation, later to C1And C2CZ operation is executed, six bit Cluster States can be successfully prepared:
Due to the above technical solutions, the present invention has the following advantages over the prior art:
1, the channel transmitted using GHZ as information the invention proposes one, both sides are that remote third party prepares more bit groups
The method of cluster state.In the present invention, every sender only grasps the information of a part, efficiently avoids the leakage of information, thus
With preferable safety.
2, using two GHZ states as quantum channel, user Alice introduces an auxiliary particle and carries out to channel the present invention
Pretreatment, Charlie according to the projection measurement result of Alice and Bob introduce four auxiliary particles and implement it is appropriate just
Operation can complete the preparation of six bit Cluster States, and the present invention can consume least quantum resource, realize six bit clusters
The preparation of state.
Detailed description of the invention
Fig. 1 is a kind of method of joint six bit Cluster States of long-range preparation based on GHZ state provided by the embodiments of the present application
Flow chart.
Fig. 2 is a kind of method of joint six bit Cluster States of long-range preparation based on GHZ state provided by the embodiments of the present application
Particle distribution figure.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
1, phase gate is controlled
It controls phase gate (CZ), it is gathered around there are two quantum bit is inputted, and is control quantum bit and target quantum respectively
Bit.Its effect is: when control quantum bit is in simultaneously with target quantum bit | it is 1 > when, the phase of the two postures is anti-
Turn π.Its corresponding matrix form are as follows:
2, controlled not-gate
Controlled not-gate CNOT (Control-NOT gate) operates two quantum bits, and second quantum bit only exists
First quantum bit be | 1 > when, carries out NOT operation, is otherwise maintained for constant.Generally with this logic gate come to two
It carries out tangling processing between quantum.
As depicted in figs. 1 and 2, the method for the joint six bit Cluster States of long-range preparation based on GHZ state, comprising:
Two sender's remote assistances, one recipient prepares the form of six bit Cluster State of target are as follows:
Wherein, coefficient a0,a1,a2,a3For plural and they meet normalizing condition, phase theta1,θ2,θ3[0,2 π) it
Between.Alice knows the amplitude information a of Cluster State to be prepared0,a1,a2,a3With a part of phase informationBob
Know another part phase information of state to be prepared
Charlie does not know about state to be prepared.
Sender Alice, Bob and recipient Charlie share 2 GHZ Quantum Entangled States:
Wherein Alice possesses particle A1,A2, Bob possesses particle B1,B2, Charlie possesses particle C1,C2。
The first step, amplitude modulation, Alice introduce auxiliary particle | 0 >a, and the particle A that oneself is possessed1、A2With it is auxiliary
Particle a is helped to execute positive operationPositive operationConcrete form is as follows:
Wherein
Entire quantized system at this time are as follows:
Then Alice executes single-particle measurement to auxiliary particle a, if measurement result is | 0 >aSo whole system is collapsed are as follows:
Otherwise, preparation failure
Second step, phase-modulation, Alice fractional phase information structuring measure base to particle A accordingly1A2Projection is executed to survey
Amount, measurement base are as follows:
Bob constructs corresponding measurement base to particle B according to another part phase information simultaneously1B2Execute projection measurement, measurement
Base is as follows:
Based on above two groups of measurement bases, entire quantized system are as follows:
There are four types of possible for the measurement result of Alice:Corresponding four kinds are not
Same encoded information 00,01,10,11.Also there are four types of may respectively be the measurement result of Bob simultaneously:Corresponding four kinds of encoded informations 00,01,10,11, when Alice and Bob is completed
After measurement, measurement result is sent to by recipient Charlie by classical channel.Specifically, if the measurement result of Alice isPair answer encoded information 00, the measurement result of Bob isCorresponding encoded information is that 01, Alice and Bob will be surveyed
Amount result is corresponding to be passed through classical channel at classical information and is sent to recipient Charlie, then Alice that Charlie is received and
The classical information that Bob is sent is 00 and 01, at this time the particle C in Charlie hand1、C2State then become
Third step, according to the measurement result of Alice and Bob, Charlie executes corresponding positive operation
Obtain the dibit quantum state closely related with six bit Cluster States to be prepared:
Specifically, according to the measurement result of Alice and Bob, the particle that Charlie possesses it is executedOperation:Restore intermediate quantum state corresponding with target Cluster State.WhenSoThat is Charlie is to particle C1I operation is executed, whenSoI.e.
Charlie is to particle C1Execute Z operation.It is similar therewith, whenSoI.e. Charlie is to particle
C2I operation is executed, whenSoThat is Charlie is to particle C2Execute Z operation.
The positive operation table that table 1:Charlie is executed according to the measurement result of Alice and Bob
4th step, Charlie introduce auxiliary particle, and execute corresponding replacement operator, restore six bit Cluster State of target.
Specifically, Charlie is firstly introduced into four auxiliary particlesWhole system can be rewritten into:
Then Charlie is to particle to C2And C4(C2To control quantum bit, C4For target quantum bit), C4And C6(C4
To control quantum bit, C6For target quantum bit) CNOT operation is successively executed, while to particle to C1And C3(C1For control amount
Sub- bit, C3For target quantum bit), C3And C5(C3To control quantum bit, C5For target quantum bit) successively execute CNOT
Operation, later to C1And C2CZ operation is executed, six bit Cluster States can be successfully prepared:
Each technical characteristic of embodiment described above can be combined arbitrarily, for simplicity of description, not to above-mentioned reality
It applies all possible combination of each technical characteristic in example to be all described, as long as however, the combination of these technical characteristics is not deposited
In contradiction, all should be considered as described in this specification.
The embodiments described above only express several embodiments of the present invention, and the description thereof is more specific and detailed, but simultaneously
It cannot therefore be construed as limiting the scope of the patent.It should be pointed out that coming for those of ordinary skill in the art
It says, without departing from the inventive concept of the premise, various modifications and improvements can be made, these belong to protection of the invention
Range.Therefore, the scope of protection of the patent of the invention shall be subject to the appended claims.
Claims (6)
1. a kind of method of the joint six bit Cluster States of long-range preparation based on GHZ state characterized by comprising
Two sender's remote assistances, one recipient prepares the form of six bit Cluster State of target are as follows:
Wherein, coefficient a0,a1,a2,a3For plural and they meet normalizing condition, phase theta1,θ2,θ3[0,2 π) between,
Alice knows the amplitude information a of Cluster State to be prepared0,a1,a2,a3With a part of phase informationBob knows
Another part phase information of state to be prepared Charlie
State to be prepared is not known about；
Sender Alice, Bob and recipient Charlie share 2 GHZ Quantum Entangled States:
Wherein Alice possesses particle A1,A2, Bob possesses particle B1,B2, Charlie possesses particle C1,C2；
Alice introduces auxiliary particle | 0 >a, and the particle A that oneself is possessed1、A2Positive operation is executed with auxiliary particle a
Then Alice executes single-particle measurement to auxiliary particle a, if measurement result is | 0 >aSo whole system is collapsed are as follows:
Alice measures base to particle A according to fractional phase information structuring accordingly1A2Projection measurement is executed, meanwhile, Bob is according to another
A part of corresponding measurement base of phase information construction is to particle B1B2Execute projection measurement；After completing measurement, Alice and Bob will
Measurement result is corresponding at classical information, is sent to recipient Charlie by classical channel；
According to the measurement result of Alice and Bob, Charlie executes corresponding positive operation and obtains and six bit groups to be prepared
The closely related dibit quantum state of cluster state:
Charlie introduces auxiliary particle, and executes corresponding replacement operator, restores six bit Cluster State of target.
2. the method for the joint six bit Cluster States of long-range preparation according to claim 1 based on GHZ state, feature exist
In positive to operateConcrete form is as follows:
Wherein
3. the method for the joint six bit Cluster States of long-range preparation according to claim 1 based on GHZ state, feature exist
In " Alice measures base to particle A according to fractional phase information structuring accordingly1A2Projection measurement is executed, " in, measurement base is as follows
It is shown:
4. the method for the joint six bit Cluster States of long-range preparation according to claim 1 based on GHZ state, feature exist
In " Bob constructs corresponding measurement base to particle B according to another part phase information1B2Execute projection measurement；" in, measurement base is such as
Shown in lower:
5. the method for the joint six bit Cluster States of long-range preparation according to claim 1 based on GHZ state, feature exist
In " according to the measurement result of Alice and Bob, Charlie executes corresponding positive operation and obtains and six bit groups to be prepared
The closely related dibit quantum state of cluster state:" it is specifically: root
According to the measurement result of Alice and Bob, the particle that Charlie possesses it is executedOperation:It is extensive
Multiple intermediate quantum state corresponding with target Cluster State；WhenSoI.e. Charlie is to particle
C1Execute I operation；WhenSoThat is Charlie is to particle C1Execute Z operation；With etc
Seemingly, whenSoThat is Charlie is to particle C2I operation is executed, whenThat
?That is Charlie is to particle C2Execute Z operation.
6. the method for the joint six bit Cluster States of long-range preparation according to claim 1 based on GHZ state, feature exist
In " Charlie introduces auxiliary particle, and executes corresponding replacement operator, restores six bit Cluster State of target." it is specifically:
Charlie is firstly introduced into four auxiliary particlesWhole system can be rewritten into:
Then Charlie is to particle to C2And C4(C2To control quantum bit, C4For target quantum bit), C4And C6(C4For control
Quantum bit, C6For target quantum bit) CNOT operation is successively executed, while to particle to C1And C3(C1To control quantum ratio
Spy, C3For target quantum bit), C3And C5(C3To control quantum bit, C5For target quantum bit) CNOT operation is successively executed,
Later to C1And C2CZ operation is executed, six bit Cluster States can be successfully prepared:
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| CN111555876A (en) * | 2020-05-15 | 2020-08-18 | 苏州大学 | Combined cycle remote state preparation method based on non-maximum entangled channel N-party control |
| 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 |
| CN111555877A (en) * | 2020-05-18 | 2020-08-18 | 苏州大学 | Method for remotely preparing three-bit state based on five-bit Brown state controlled multi-party combination |
| CN111555877B (en) * | 2020-05-18 | 2022-01-11 | 苏州大学 | Method for remotely preparing three-bit state based on five-bit Brown state controlled multi-party combination |
| CN112202502A (en) * | 2020-09-29 | 2021-01-08 | 苏州大学 | Single-particle-state remote preparation method based on non-maximum entangled GHZ channel |
| WO2022183809A1 (en) * | 2021-03-05 | 2022-09-09 | 苏州大学 | Joint and accelerated remote state preparation method based on undetermined terminal |
| CN114679225A (en) * | 2022-05-10 | 2022-06-28 | 成都理工大学 | Preparation method for asymmetric controlled cycle combined remote quantum state under noise |
| CN114679225B (en) * | 2022-05-10 | 2023-08-29 | 成都理工大学 | Preparation method of asymmetric controlled-cycle combined remote quantum state under noise |
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