CN106059680A - Method for transmitting two-particle entangled state in multi-hop way - Google Patents

Method for transmitting two-particle entangled state in multi-hop way Download PDF

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CN106059680A
CN106059680A CN201610539806.7A CN201610539806A CN106059680A CN 106059680 A CN106059680 A CN 106059680A CN 201610539806 A CN201610539806 A CN 201610539806A CN 106059680 A CN106059680 A CN 106059680A
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particle
state
node
entangled
transmission
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CN106059680B (en
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余旭涛
熊佩颖
张在琛
邹珍珍
王侃
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Southeast University
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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
    • H04B10/70—Photonic quantum communication
    • 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
    • H04B10/90—Non-optical transmission systems, e.g. transmission systems employing non-photonic corpuscular radiation

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  • Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Electromagnetism (AREA)
  • Engineering & Computer Science (AREA)
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Abstract

The invention discloses a method for transmitting a two-particle entangled state in a multi-hop way. In the method, an intermediate node is introduced to realize teleportation of the two-particle entangled state between two nodes which are relatively far away from each other in a quantum communication network, and auxiliary particles are introduced to a destination node to successively recover a two-particle state to be transmitted by unitary transformation. Through adoption of the method for transmitting the two-particle entangled state in the multi-hop way, safe and reliable transmission of quantum information can be provided. Moreover, the auxiliary particles are introduced to the destination node to perform state recovery, so that the successful transmission probability of the two-particle entangled state among a plurality of nodes is increased.

Description

A kind of method of multi-hop transmission two-particle entangled state
Technical field
The invention belongs to quantum communications field, a kind of method being specifically related to multi-hop transmission two-particle entangled state, utilize two Particle fraction Entangled State and maximum W state are as quantum entanglement channel, it is achieved two-particle entangled state two distant nodes it Between multi-hop transmission.
Background technology
Quantum information is field of scientific study popular in recent years, generally includes quantum calculation and quantum communications.At quantum In communication, quantum teleportation is a kind of most important and widely used method.Quantum communications utilize quantum state as carrier Transmission information, is a kind of brand-new communication mode, there is huge application prospect.In the last few years, researchers will research Scope expands to the Teleportation of multiparticle from simple single-particle Teleportation, expands to part from maximal entangled state and tangles State.In quantum communication network, it is usually present two kinds of channels, i.e. quantum channel and classical wireless channel.Quantum state is by tangling Particle is to transmission of quantum information in free space in the way of Teleportation.Classical information in network, such as measurement result Then transmitted by classical wireless channel.
Simultaneously as in quantum communication network, have the problem of a highly important quantum teleportation to need to solve, That is: source node cannot realize enjoying the resource tangled, in order to realize phase with other all destination nodes in quantum communication network Teleportation between two nodes farther out, introduces multiple intermediate node, and every pair of adjacent node is shared a pair and tangled source, with This establishes source node to the quantum path between destination node.Therefore, it is achieved multiple internodal quantum multi-hop transmission sides Case has great importance.
Summary of the invention
Goal of the invention: in order to solve problems of the prior art, the present invention proposes a kind of multi-hop transmission two particle and entangles The method twining state, is possible not only to provide the transmission of reliably and securely quantum information, and improves two by introducing auxiliary particle Entangled is at the quantum communication network successful probability of multiple inter-node transmission.
Technical scheme: to achieve these goals, the method for multi-hop transmission two-particle entangled state in the present invention, including following Step:
(1) introducing intermediate node between a source node and a destination node, from source node to destination node, arbitrary neighborhood two saves Point shares a pair two particle fraction Entangled States and a pair maximum W state, builds quantum entanglement channel；
(2) source node transmits two-particle entangled state along intermediate node successively until destination node.
Specifically, in step (2), source node transmits two-particle entangled state along intermediate node successively until destination node, wraps Include herein below:
Except destination node, to each node, the grain to one of them particle state to be transmitted at this node with maximum W state Son carries out Bell base measurement, and the particle of another particle state to be transmitted and two particle fraction Entangled States is carried out Bell base measurement； The particle of described maximum W state refer to the next node of this node at particle constitute the particle of maximum W state, described two particle unit The particle of point Entangled State refer to the next node of this node at particle constitute the particle of two particle fraction Entangled States；
At the next node of this node, select and at a upper node, a particle of the maximum W state of particle composition carries out shape State is measured, and judges upper hop particle state whether transmission success according to state measurement, if there is successful probability, then foundation The Bell base measurement result of upper hop is chosen corresponding Pauli matrices two particle waiting for transmission to this node and is carried out state transformation；Institute State one in this node two particle waiting for transmission be with a upper node at particle constitute another particle of maximum W state, another Individual for a upper node at particle constitute the particle of two particle fraction Entangled States；
For destination node, after state transformation the state of two particle waiting for transmission then for the purpose of two particle entangleds at node State.
If more specifically, particle state measurement result is | 1 ＞, the most there is not the probability of transmission success；If particle state is surveyed Measuring result is | 0 ＞, then there is the probability of transmission success.
When two-particle entangled state is transferred to destination node, there is two Particle Delivery not yet successfully situation, therefore, the present invention The two-particle entangled state of not yet transmission success by introducing auxiliary particle at destination node, is recovered by method the most further Operation, particularly as follows: select suitable unitary transformation U according to the Bell base measurement result of remaining each node in addition to destination node, Utilize the two-particle entangled state at destination node that the two-particle entangled state of transmission at source node is recovered.
Further, if the state of auxiliary particle is | during 1 ＞, then cannot two particle entangleds of transmission at Restorer varieties node State；If the state of auxiliary particle is | 0 > time, then the two-particle entangled state of transmission at success Restorer varieties node.
Beneficial effect: the method for the multi-hop transmission two-particle entangled state in the present invention, realizes two by introducing intermediate node Teleportation between two nodes that Entangled is apart from each other in quantum communication network, it is provided that reliably and securely The transmission of quantum information；Further, by introducing auxiliary particle in destination node and utilizing unitary transformation successfully to recover to be wanted Two states of transmission, improve two-particle entangled state at the successful probability of multiple inter-node transmission.
Accompanying drawing explanation
Fig. 1 is the multi-hop transmission illustraton of model of the present invention；
Fig. 2 be nodes be multi-hop transmission illustraton of model when 3；
Fig. 3 be nodes be multi-hop Quantum Teleportation layout when 3.
Detailed description of the invention
Below in conjunction with case study on implementation, the present invention is further described.
Multi-hop transmission scheme in the present invention is set up under the background of quantum cordless communication network.As it is shown in figure 1, source node There are two particle states 1,2 to be transmitted in Alice (node N=1) place, needs to transmit this to two-particle entangled state | ψ12>=α | 00 >12+β|11〉12(||α2||+||β2| |=1) to distant destination node Bob (node N=M+1) place, scheme introduces M- 1 intermediate node (node N=2 to node N=M), then co-exist in M+1 node on transmission path.The most adjacent two nodes are altogether Enjoy a pair two particle fraction Entangled StatesWherein 0 < n < 1, and a pair maximum W stateAs quantum entangled source, form quantum entanglement channel.
Specifically introducing the present invention program as a example by 3 node multi-hop transmissions in Fig. 2, Fig. 3, in figure, Alice is source node, Node for the purpose of Bob, Candy is introduced intermediate node, there is particle 1,2 waiting for transmission and maximum W at source node Alice The particle 3 of state and the particle 6 of two particle fraction Entangled States；Exist at intermediate node Candy and particle 3 at source node Alice Form the particle 4,5 of maximum W state, and particle 6 form the particle 7 of two particle fraction Entangled States, with destination node Bob at particle 9, 10 particles 8 forming maximum W state, with the particle 11 that particle 12 forms two particle fraction Entangled States；Exist at destination node Bob The particle 9,10 of big W state, the particle 12 of two particle fraction Entangled States, and the auxiliary particle Aux introduced.Source node Alice needs Transmit a pair two-particle entangled state | ψ12＞=α | 00 ＞12+β|11〉12To distant destination node Bob.In conjunction with Fig. 2, Fig. 3, The method of the multi-hop transmission two-particle entangled state in the present invention comprises the following steps:
(1) introducing intermediate node between a source node and a destination node, from source node to destination node, arbitrary neighborhood two saves Point shares a pair two particle fraction Entangled States and a pair maximum W state, builds quantum entanglement channel.
Alice Yu Candy shares a pair two particle fraction Entangled States and a pair maximum W state, two particle fraction Entangled States State is:The state of maximum W state is: Candy Yu Bob shares a pair two particle fraction Entangled States and a pair maximum W state, and the state of two particle fraction Entangled States is:The state of maximum W state is: Thus establish the quantum entanglement channel of adjacent node.
(2) source node transmits two-particle entangled state along intermediate node successively until destination node is except destination node, right Each node, carries out Bell base measurement, to another to the particle of one of them particle state to be transmitted at this node with maximum W state The particle of individual particle state to be transmitted and two particle fraction Entangled States carries out Bell base measurement；The particle of described maximum W state refers to With the particle that particle at the next node of this node constitutes maximum W state, the particle of described two particle fraction Entangled States refer to At the next node of this node, particle constitutes the particle of two particle fraction Entangled States；At the next node of this node, select with At a upper node, a particle of the maximum W state of particle composition carries out state measurement, and judges upper hop according to state measurement Particle state whether transmission success, if there is successful probability, then chooses corresponding bubble according to the Bell base measurement result of upper hop Profit matrix two particle waiting for transmission to this node carries out state transformation；In described node two particle waiting for transmission one be with At a upper node, particle constitutes another particle of maximum W state, another for a upper node at particle constitute two particle fraction The particle of Entangled State；For destination node, after state transformation the state of two particle waiting for transmission then for the purpose of at node two Sub-Entangled State.
21) to the particle state to be transmitted 1 at source node Alice and maximum W state particle 3, and another particle to be transmitted One particle 6 of state 2 and two particle fraction Entangled States carries out Bell base measurement respectively.
For intermediate node Candy, with source node Alice at particle 3 form in two particles of maximum W state optional one Particle judges upper hop particle state whether transmission success for state measurement, and the present embodiment selection particle 4, another particle is then Particle to be transmitted, is particle 5 in the present embodiment；Measure the state of particle 4, and utilize the condition adjudgement upper hop of particle 4 The transmission of particle state is the most successful, if the state of particle 4 is | and 1 >4, the probability of two-particle entangled state transmission success is 0, and quantum passes State failure；If the state of particle 4 is | 0 >4, then there is successful probability, now choose accordingly according to Bell base measurement result Two particles 5,7 waiting for transmission at next node Candy are operated by Pauli matrices.
Assume m1,m3,m2,m6Representing Bell base measurement result, at each node, the formula of corresponding Pauli matrices isWherein σx, σy, σzRepresent standard Pauli matrices,Represent m3Value negate, Represent m1And m2Value take XOR.Then the operation to particle 5 and 7 is: It is right to represent Particle 5 carries out σxOperation,Represent and particle 7 is carried out σzOperation.Then, the state of tangling of particle 5,7 can be converted into α | and 00 >57+nβ|11>57Or n α | 00 >57+β|11>57.Bell base measurement result correspondence m1,m3,m2,m6Be expressed as follows shown in table 1, its In every time Bell base measurement result have 4 kinds of situations: | Φ+>、|Φ->、|Ψ->、|Ψ+>。
Table 1Bell base measurement result correspondence m1,m3,m2,m6Value
22) step 21 is used) identical mode is to 5,8 and 7,11 points of the particle at the next-hop node Candy of source node Do not carry out Bell base measurement, i.e. to particle state 5 to be transmitted and the particle 8 of maximum W state, and another particle state 7 to be transmitted with The particle 11 of two particle fraction Entangled States carries out Bell base measurement respectively.Can determine whether whether the second jumping passes state by measuring particle 9 Success, when particle 9 state is | 1 >9, the probability of two-particle entangled state transmission success is 0, Teleportation failure；If the shape of particle 9 State is | 0 >9, there is certain probability of success in two Particle Delivery, chooses corresponding Pauli matrices according to Bell base measurement resultTwo particles 10 and 12 waiting for transmission at operation destination node Bob, transmission success obtains Particle state α | 00 >1012+β|11>1012, now it is not required to carry out again any particle manipulation；Otherwise, two Particle Delivery not yet successfully shape Then it is converted into α to state | and 00 >1012+n2β|11>1012Or n2α|00>1012+β|11>1012。
(3) it is transferred to destination node Bob when two-particle entangled state, for two particles not yet successfully state, due to now Particle state be not the particle state that source node initially transmits, by introducing auxiliary particle in destination node, and according to each node Bell base measurement result select suitable unitary transformation U can recover two-particle entangled state α | 00 >+β | 11 of initially transmission >。
After assuming to carry out i jump set state, not yet passing the successful particle state of state at destination node is α | 00 >+ni-2jβ | 11 > or ni-2jα | 00 >+β | 11 >, wherein j=0,1,2 ..., [(i-1)/2], additionally [(i-1)/2] represent (i-1)/2 divide exactly portion Point.
Postulated particle state is α | 00 >+ni-2jβ | 11 >, then the form of U is as follows:
U = n i - 2 j 0 0 0 0 1 - n 2 ( i - 2 j ) 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 - n 2 ( i - 2 j ) 0 0 0 1 0 0 0 0 0 0 0 0 0 0 n i - 2 j 0 0 0 0 0 0 1 0 0 0 0 0 0 n i - 2 j 0 1 - n 2 ( i - 2 j ) - - - ( 1 )
Postulated particle state is ni-2jα | 00 >+β | 11 >, then the form of U is as follows:
U = 1 0 0 0 0 0 0 0 0 n i - 2 j 0 0 0 0 1 - n 2 ( i - 2 j ) 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 - n 2 ( i - 2 j ) 0 0 0 0 n i - 2 j 0 0 0 0 0 0 0 0 1 - - - ( 2 )
As a example by i=2 in the present embodiment, i.e. carry out 2 times passing after state (as shown in Figure 2), at destination node Bob not yet Successfully state is then converted into α | and 00 >1012+n2β|11>1012And n2α|00>1012+β|11>1012.Introduce auxiliary particle Aux, to grain Son 10,12 and Aux carries out corresponding U operation, can recover two-particle entangled state α | 00 >+β | 11 of initially transmission >, the shape of U Formula following (taking i=2, j=0 in corresponding formula (1), (2)):
Or
Now, also by the state measuring auxiliary particle Aux, it can be determined that whether two-particle entangled state finally transmits to become Merit.When the state recording auxiliary particle Aux is | 1 >AuxTime, the final bust this of two-particle entangled state；When recording auxiliary particle The state of Aux is | 0 >AuxTime, showing to have recovered the two-particle entangled state of initially transmission, two-particle entangled state finally transmits Success.

Claims (5)

1. the method for a multi-hop transmission two-particle entangled state, it is characterised in that comprise the following steps:
(1) introducing intermediate node between a source node and a destination node, from source node to destination node, arbitrary neighborhood two node is altogether Enjoy a pair two particle fraction Entangled States and a pair maximum W state, build quantum entanglement channel；
(2) source node transmits two-particle entangled state along intermediate node successively until destination node.
The method of multi-hop transmission two-particle entangled state the most according to claim 1, it is characterised in that source joint in step (2) Point transmits two-particle entangled state successively along intermediate node until destination node, including herein below:
Except destination node, to each node, the particle of one of them particle state to be transmitted at this node with maximum W state is entered Row Bell base is measured, and the particle of another particle state to be transmitted and two particle fraction Entangled States is carried out Bell base measurement；Described The particle of maximum W state refer to the next node of this node at particle constitute the particle of maximum W state, described two particle fraction entangle Twine the particle of state refer to the next node of this node at particle constitute the particle of two particle fraction Entangled States；
At the next node of this node, select and at a upper node, a particle of the maximum W state of particle composition carries out state survey Amount, and judge upper hop particle state whether transmission success according to state measurement, if there is successful probability, then according to upper one The Bell base measurement result jumped is chosen corresponding Pauli matrices two particle waiting for transmission to this node and is carried out state transformation；Described In node two particle waiting for transmission one be with a upper node at particle constitute another particle of maximum W state, another is The particle of two particle fraction Entangled States is constituted with particle at a upper node；
For destination node, after state transformation the state of two particle waiting for transmission then for the purpose of two-particle entangled state at node.
The method of multi-hop transmission two-particle entangled state the most according to claim 2, it is characterised in that if particle state is measured Result is, the most there is not the probability of transmission success；If particle state measurement result is, then there is the probability of transmission success.
The method of multi-hop transmission two-particle entangled state the most as claimed in any of claims 1 to 3, it is characterised in that The method is further comprising the steps of:
When two-particle entangled state is transferred to destination node, there is two Particle Delivery not yet successfully situation, introduce in destination node Auxiliary particle, and select suitable unitary transformation U, profit according to the Bell base measurement result of remaining each node in addition to destination node With the two-particle entangled state at destination node, the two-particle entangled state of transmission at source node is recovered.
The method of multi-hop transmission two-particle entangled state the most according to claim 4, it is characterised in that if the shape of auxiliary particle State isTime, then cannot the two-particle entangled state of transmission at Restorer varieties node；If the state of auxiliary particle isTime, then success is extensive The two-particle entangled state of transmission at multiple source node.
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CN109379183B (en) * 2018-09-25 2021-03-23 苏州大学张家港工业技术研究院 Multi-hop lossless invisible state transfer method based on non-maximum entangled chain channel
CN110350968A (en) * 2019-07-16 2019-10-18 苏州大学 Chain type Teleportation method is tieed up based on the d that relay node measurement result is sent at random
CN110350968B (en) * 2019-07-16 2020-06-30 苏州大学 D-dimensional chain type invisible state transferring method based on random sending of relay node measurement result
CN114422120A (en) * 2021-12-21 2022-04-29 苏州大学 High-dimensional multi-hop lossless invisible transmission method for channel modulation weight transfer

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