CN103618695A - Total probability arbitrary multiparty JRSP method - Google Patents

Abstract

The invention provides a total probability arbitrary multiparty JRSP method. According to the method, a core sender constructs a real part measurement base in accordance with real part information of quantum states needing to be prepared, particles owned by the core sender are measured, and measuring results are sent to corresponding auxiliary senders and receivers through classical channels; all the auxiliary senders construct imaginary part measurement bases by the adoption of the measuring results and owned imaginary part information, particles owned by the auxiliary senders are measured respectively, and measuring results are sent to the receivers through classical channels; at last, the receivers conduct certain unitary operation on the particles in hands according to the measuring results of the core sender and the measuring results of all the auxiliary senders, and the particles needing to be prepared are obtained. By means of the total probability arbitrary multiparty JRSP method, the methods of quantum information fragmentation, quantum entanglement and quantum measurement are used, arbitrary multiparty JRSP is achieved, and the method is safe and reliable, flexible and universal, and good in practical value.

Description

A kind of full probability is the long-range combined preparation process of quantum state in many ways arbitrarily

Technical field

The invention belongs to communication technical field, specifically refer to a kind of full probability long-range combined preparation process of quantum state in many ways arbitrarily.

Background technology

As everyone knows, communication channel transmission at present is digital signal or analog signal.Other that mix up into while having nonideal frequency response characteristic, noise jamming and signal by transmission due to channel disturb, and have damaged transmitted signal and the signal mode generation distortion that makes to receive or the digital signal code element generation mistake that makes reception.For this type of, disturb, mainly by two kinds of modes, guarantee at present the correct transmission of channel: be the Performance and quality that improves circuit and transmission equipment on the one hand, as adopted optical fiber; To adopt error control strategy on the other hand, as cyclic redundancy check method etc.Yet improving circuit and equipment needs the renewal of technology and a large amount of investments, use error check inevitably to waste the communication resource, slowed down communication speed.Therefore, the correct transmission of guarantee information is classic network communication urgent need to solve the problem always.Development along with quantum information technology, some network communication methods based on Quantum Properties are proposed successively, as quantum-key distribution (QKD), Quantum Secure Direct Communication (QSDC), quantum secret sharing (QSS) and quantum teleportation (QT) etc.These communication meanss are mainly usingd microcosmic particle as information carrier, and by feat of its more distinctive quantum nature, as coherence, Entanglement etc., the interference while avoiding transmitting, has unconditional fail safe, accuracy.Under this background, the transmission problem that utilizes quantum information technology to solve information is more and more paid close attention to.

The long-range preparation of quantum state (RSP) is the derivative of quantum teleportation (QT), and both differences are only whether know transmitted quantum state, the former to know in advance transmitted be what quantum state and the latter does not know completely.Particularly, RSP refers to based on quantum entanglement characteristic, under the condition of the known quantum state information that need prepare of transmit leg, assists distant place recipient to prepare this quantum state.Compare quantum teleportation, the long-range preparation of quantum state has better potential application foreground, is therefore subject in recent ten years the extensive concern of Chinese scholars.Since the people such as calendar year 2001 Bennett have proposed first RSP agreement, all kinds of RSP agreements are constantly proposed, and RSP has also experienced one to be developed into and prepare multiple particle state from preparing single-particle state, from probability preparation, develops into process prepared by certainty (full probability).

In addition, from participant, in most of RSP, only have a transmit leg and a recipient.Consider the fail safe of preparation, part Study person starts to pay close attention to and how to realize a plurality of senders and combine the problem that transmits quantum state to a recipient.The long-range novel preparation technology that preparation (JRSP) proposes in order to address this problem just, the quantum state information that it requires the shared need of a plurality of transmit legs to prepare of combining of quantum state.Due to need, preparing quantum state information is not to be monopolized by a certain sender, but shares between all transmit legs, so higher than general RSP on JRSP safety theory.With regard to current research, most of JRSP schemes only rest on two sides and combine preparation above, and the long-range preparation of quantum state rarely has report in many ways arbitrarily, and its reason is to be difficult to find appropriate universal measurement base and correct substep preparation strategy.Yet in actual applications, we know with respect to two sides and combine preparation, in many ways combine arbitrarily preparation more flexibly, safety, also have more practical application meaning.The present invention is intended to by ingenious structure real part, imaginary part universal measurement base, in conjunction with substep preparation strategy, has proposed a kind of full probability long-range combined preparation process of quantum state in many ways arbitrarily.The method, in the presence of any N transmit leg, finally can obtain required quantum state, and probability is 1(full probability by combining the mode recipient of preparation).

Summary of the invention

Technical problem to be solved by this invention is to overcome the deficiencies in the prior art, provides a kind of full probability long-range combined preparation process of quantum state in many ways arbitrarily.Described method utilizes EPR to as quantum channel, and by structure real part, imaginary part universal measurement base, in conjunction with substep preparation strategy, thereby quantum state is long-range in many ways arbitrarily combines preparation in realization, to improve fail safe and the flexibility of long-range preparation.

In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is: a kind of full probability is the long-range combined preparation process of quantum state in many ways arbitrarily, and total N+1 of described method participant, comprises N sender and a recipient; In N sender, a sender is core sender, and another N-1 sender is auxiliary sender; N is natural number;

Core sender, auxiliary sender, recipient share N EPR couple, are expressed as follows:

${|Q\&rang;}_{A_1{B}_1{A}_2{B}_2...A_{N-1}{B}_{N-1}{A}_{N}C}={|\mathrm{EPR}\&rang;}_{A_1{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000410133910000011.png,HDA0000410133910000012.png"\; state="\{\{state\}\}">B</figure-callout>}}_1}{|\mathrm{EPR}\&rang;}_{A_2{B}_2}...{|\mathrm{EPR}\&rang;}_{A_{1N-1}{B}_{N-1}}{|\mathrm{EPR}\&rang;}_{A_{N}C}$

Wherein

${|\mathrm{EPR}\&rang;}_{A_k{B}_k}=\frac{1}{\sqrt{2}}{\left(\right|00\&rang;+|11\&rang;)}_{A_k{B}_k},1\&le;k\&le;N$

Core sender has N particle, is respectively A ₁, A ₂..., A _j, A _n; Each auxiliary sender has and A _jcorresponding B _jparticle, j is auxiliary sender's sequence number, 1≤j≤N-1; Recipient has C particle, C particle and A _nparticle is corresponding;

Suppose and need the quantum state of preparation to be

core sender knows quantum state | the real part information of φ > a, b}, and auxiliary sender knows quantum state | the imaginary part information of φ >

and

The concrete steps of described method are as follows:

Step 1, core sender according to known to quantum state real part information a, b} structure real part is measured base;

Step 2, core sender measures its N having particle, and the measurement result of a described N particle is sent to respectively to N-1 auxiliary sender and recipient, and each auxiliary sender and recipient receive only the measurement result of a corresponding particle; When each auxiliary sender and recipient receive measurement result, the particle that each auxiliary sender and recipient have produces and tangles;

Step 3, each auxiliary sender according to core sender's particle measurement result and known to quantum state imaginary part information, structure is measured base;

Step 4, according to the measurement base described in step 3, each auxiliary sender measures the particle that it has, and the measurement result of described particle is sent to recipient;

Step 5, recipient receives core sender and 1 auxiliary sender's of N – measurement result, chooses unitary operator, and the particle that recipient is had carries out operation at the tenth of the twelve Earthly Branches, obtains the quantum state of required preparation | φ >.

In step 1, described real part is measured base by 2 ⁿindividual quadrature quantum state forms, and its mathematical form can be expressed as

${\left\{{(-1)}^{i_1}a\right|i_1{i}_2...i_N\&rang;}_{A_1{,A}_2,...,A_N}+b{|\stackrel{\&OverBar;}{i_1{i}_2}...\stackrel{\&OverBar;}{i_N}\&rang;}_{A_1,A_2,...,A_N}|i_k\&Element;\{\mathrm{0,1}\},\stackrel{\&OverBar;}{i_k}=1-i_k,1\&le;k\&le;N\}.$

In step 2, described measurement result is: l ₁l ₂l _n, and l _k∈ { 0,1}, 1≤k≤N.

In step 3, described measurement base table is shown:

Wherein: l _jfor the j position of core sender measurement result,

be j the part imaginary part information known to auxiliary sender, and

In step 5, described operation at the tenth of the twelve Earthly Branches refers to: from I, and Z, X, ZX} chooses a kind of operation in operation tetra-tenth of the twelve Earthly Branches; This operation at tenth of the twelve Earthly Branches

be expressed as follows:

Wherein,

I=|0><0|+|1>LEs sT.LTssT.LT1|, Z=|0><0|-|1>LEs sT.LTssT.LT1|, X=|0><1|+|1>LEs sT.LTssT.LT0|; m ₁, m ₂, m _j..., m _n-1the measurement result that represents respectively N-1 auxiliary sender, and m _j{ 0,1}, ⊕ represents binary system xor operation to ∈.

The invention has the beneficial effects as follows: the present invention proposes a kind of full probability long-range combined preparation process of quantum state in many ways arbitrarily.The real part information structuring real part that in described method, core sender prepares quantum state according to need is measured base, and the particle that it is had is measured, and by classical channel, measurement result is sent to corresponding auxiliary sender and recipient; The imaginary part information structuring imaginary part measurement base that each auxiliary sender utilizes measurement result and has, measures the particle having respectively, and by classical channel, measurement result is sent to recipient; Finally, recipient carries out some operation at the tenth of the twelve Earthly Branches according to particle in core sender and each auxiliary sender's measurement result opponent, obtains and need prepare particle.The present invention has utilized that quantum information is cut apart, quantum entanglement and quantum method of measurement, realizes arbitrarily in many ways that quantum state is long-range combines preparation, and its method safety is reliable, agile and all-purpose, has good practical value.

Accompanying drawing explanation

Fig. 1 is the universe network topological diagram of the inventive method.

Fig. 2 is the quantum wire figure of the inventive method.

Embodiment

Below in conjunction with accompanying drawing, a kind of full probability that the present invention is proposed arbitrarily in many ways the long-range combined preparation process of quantum state be elaborated:

Universe network topological structure of the present invention as shown in Figure 1, is specifically described below:

Suppose and need the quantum state of preparation to be

total N+1 of participant, comprises N sender and a recipient; In N sender, a sender is core sender, and another N-1 sender is auxiliary sender; N is natural number.Quantum channel by N EPR to forming, ${|Q\&rang;}_{A_1{B}_1{A}_2{B}_2...A_{N-1}{B}_{N-1}{A}_{N}C}={|\mathrm{EPR}\&rang;}_{A_1{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000410133910000011.png,HDA0000410133910000012.png"\; state="\{\{state\}\}">B</figure-callout>}}_1}{|\mathrm{EPR}\&rang;}_{A_2{B}_2}...{|\mathrm{EPR}\&rang;}_{A_{1N-1}{B}_{N-1}}{|\mathrm{EPR}\&rang;}_{A_{N}C}.$ In Fig. 1, core sender S is in center, and it has A ₁, A ₂..., A _nparticle; Each auxiliary sender T _jbe positioned at core sender's surrounding, have respectively B _jparticle, j is auxiliary sender's sequence number, is natural number, 1≤j≤N-1; Recipient D is positioned at the right-hand of core sender, has C particle.

As shown in Figure 2, its execution sequence is for from left to right for major technique step of the invention process, and concrete steps are as follows:

The first step, core sender S according to known to quantum state real part information { a, b} structure is measured base, ${\left\{{(-1)}^{i_1}a\right|i_1{i}_2...i_N\&rang;}_{A_1,A_2,...,A_N}+b{|\stackrel{\&OverBar;}{i_1{i}_2}...\stackrel{\&OverBar;}{i_N}\&rang;}_{A_1,A_2,...,A_N}|i_k\&Element;\{\mathrm{0,1}\},\stackrel{\&OverBar;}{i_k}=1-i_k,1\&le;k\&le;N\}.$ For setting forth conveniently, make N=3, the measurement base of S structure

for:

$\left(\begin{array}{c}{|u_{000}\&rang;}_{A_1{A}_2{A}_3}\\ {|u_{001}\&rang;}_{A_1{A}_2{A}_3}\\ {|u_{010}\&rang;}_{A_1{A}_2{A}_3}\\ {|u_{011}\&rang;}_{A_1{A}_2{A}_3}\\ {|u_{100}\&rang;}_{A_1{A}_2{A}_3}\\ {|u_{101}\&rang;}_{A_1{A}_2{A}_3}\\ {|u_{110}\&rang;}_{A_1{A}_2{A}_3}\\ {|u_{111}\&rang;}_{A_1{A}_2{A}_3}\end{array}\right)=\left(\begin{array}{cccccccc}a& 0& 0& 0& 0& 0& 0& b\\ 0& a& 0& 0& 0& 0& b& 0\\ 0& 0& a& 0& 0& b& 0& 0\\ 0& 0& 0& a& b& 0& 0& 0\\ 0& 0& 0& -b& a& 0& 0& 0\\ 0& 0& -b& 0& 0& a& 0& 0\\ 0& -b& 0& 0& 0& 0& a& 0\\ -b& 0& 0& 0& 0& 0& 0& a\end{array}\right)=\left(\begin{array}{c}{|000\&rang;}_{A_1{A}_2{A}_3}\\ {|001\&rang;}_{A_1{A}_2{A}_3}\\ {|010\&rang;}_{A_1{A}_2{A}_3}\\ {|011\&rang;}_{A_1{A}_2{A}_3}\\ {|100\&rang;}_{A_1{A}_2{A}_3}\\ {|101\&rang;}_{A_1{A}_2{A}_3}\\ {|110\&rang;}_{A_1{A}_2{A}_3}\\ {|111\&rang;}_{A_1{A}_2{A}_3}\end{array}\right)$

Second step, according to the measurement base of constructing in the first step, core sender S measures the particle having, and by measurement result l ₁l ₂l ₃by classical channel, send to auxiliary sender T ₁, T ₂with recipient D.Before measurement, quantum channel be expressed as:

${|Q\&rang;}_{A_1{B}_1{A}_2{B}_2{A}_{3}C}=\frac{1}{2\sqrt{2}}\underset{{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA0000410133910000011.png,HDA0000410133910000012.png"\; state="\{\{state\}\}">l</figure-callout>}}_1=0}{\overset{1}{\mathrm{\&Sigma;}}}\underset{l_2=0}{\overset{1}{\mathrm{\&Sigma;}}}\underset{l_3=0}{\overset{1}{\mathrm{\&Sigma;}}}{|u_{l_1{l}_2{l}_3}\&rang;}_{A_1{A}_2{A}_3}{|L_{l_1{l}_2{l}_3}\&rang;}_{B_1{B}_{2}C}$

Wherein

concrete form is:

${|L_{000}\&rang;}_{B_1{B}_{2}C}=a{|000\&rang;}_{B_1{B}_{2}C}+b{|111\&rang;}_{B_1{B}_{2}C}$

${|L_{001}\&rang;}_{B_1{B}_{2}C}=a{|001\&rang;}_{B_1{B}_{2}C}+b{|110\&rang;}_{B_1{B}_{2}C}$

${|L_{010}\&rang;}_{B_1{B}_{2}C}=a{|010\&rang;}_{B_1{B}_{2}C}+b{|101\&rang;}_{B_1{B}_{2}C}$

${|L_{011}\&rang;}_{B_1{B}_{2}C}=a{|011\&rang;}_{B_1{B}_{2}C}+b{|100\&rang;}_{B_1{B}_{2}C}$

${|L_{100}\&rang;}_{B_1{B}_{2}C}=a{|100\&rang;}_{B_1{B}_{2}C}-b{|011\&rang;}_{B_1{B}_{2}C}$

${|L_{101}\&rang;}_{B_1{B}_{2}C}=a{|101\&rang;}_{B_1{B}_{2}C}-b{|010\&rang;}_{B_1{B}_{2}C}$

${|L_{110}\&rang;}_{B_1{B}_{2}C}=a{|110\&rang;}_{B_1{B}_{2}C}-b{|001\&rang;}_{B_1{B}_{2}C}$

${|L_{111}\&rang;}_{B_1{B}_{2}C}=a{|111\&rang;}_{B_1{B}_{2}C}-b{|000\&rang;}_{B_1{B}_{2}C}$

After measurement completes, T ₁, T ₂the particle having with D tangles generation, and state is now

The 3rd step, after obtaining the measurement result of core sender S, auxiliary sender T ₁according to the l in the measurement result of S ₁and the imaginary part information known to own

structure is measured base; In like manner, auxiliary sender T ₂according to l ₂with construct the measurement base of oneself.Its computing formula is:

According to different situations, measurement is chosen as follows:

(1) if l ₁l ₂l ₃=000or001, T ₁, T ₂the measurement base expression formula of choosing is

(2) if l ₁l ₂l ₃=110or111, T ₁, T ₂the measurement base expression formula of choosing is

(3) if l ₁l ₂l ₃=010or011, T ₁the measurement base of choosing is

T ₂the measurement base of choosing is

(4) if l ₁l ₂l ₃=100or101, T ₁the measurement base of choosing is

T ₂the measurement base of choosing is

The 4th step, supposes the measurement result l of core sender S ₁l ₂l ₃=000, assist sender T ₁, T ₂the particle having with recipient D state now can be expressed as:

${|L_{000}\&rang;}_{B_1{B}_{2}C}=a{|000\&rang;}_{B_1{B}_{2}C}+b{|111\&rang;}_{B_1{B}_{2}C}$

According to the measurement base of constructing in the 3rd step,

again write as following form:

T ₁, T ₂measure respectively one's own particle, and by classical channel by measurement result m ₁m ₂send to D.

The 5th step, at core sender S and auxiliary sender T ₁, T ₂after measurement, the particle that recipient D has has just comprised all information that need the quantum state of preparation.According to S and T ₁, T ₂measurement result, D utilizes following formula to calculate

$R_{l_1{l}_2{l}_3{m}_1{m}_2}=Z^{l_3\&CirclePlus;{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="HDA0000410133910000011.png,HDA0000410133910000012.png"\; state="\{\{state\}\}">m</figure-callout>}}_1\&CirclePlus;m_2}{\mathrm{<figure-callout\; id="1"\; label="X\; l"\; filenames="HDA0000410133910000011.png,HDA0000410133910000012.png"\; state="\{\{state\}\}">X</figure-callout>}}^{l_{}}.$

Then, D basis

choose corresponding operation at the tenth of the twelve Earthly Branches, to having single-particle C, operate, can obtain needing the quantum state of preparation.According to l ₁l ₂l ₃m ₁m ₂different situations, the tenth of the twelve Earthly Branches, the selection of operation referred to table 1.

The operation at the tenth of the twelve Earthly Branches that table 1 adopts for different measurement result recipient D

Claims (4)

1. the full probability long-range combined preparation process of quantum state in many ways arbitrarily, is characterized in that, total N+1 of described method participant, comprises N sender and a recipient; In N sender, a sender is core sender, and another N-1 sender is auxiliary sender; N is natural number;

Core sender, auxiliary sender, recipient share N EPR couple;

Core sender has N particle, is respectively A ₁, A ₂..., A _j, A _n;

Each auxiliary sender has and A _jcorresponding B _jparticle, j is auxiliary sender's sequence number, 1≤j≤N-1;

Recipient has C particle, C particle and A _nparticle is corresponding;

Suppose and need the quantum state of preparation to be

core sender knows quantum state | the real part information of φ > a, b}, and auxiliary sender knows quantum state | the imaginary part information of φ > and

The concrete steps of described method are as follows:

Step 1, core sender according to known to quantum state real part information a, b} structure real part is measured base;

Step 2, core sender measures its N having particle, and the measurement result of a described N particle is sent to respectively to corresponding N-1 auxiliary sender and recipient, and each auxiliary sender and recipient receive only the measurement result of a corresponding particle; When each auxiliary sender and recipient receive measurement result, the particle that each auxiliary sender and recipient have produces and tangles;

Step 3, each auxiliary sender according to core sender's particle measurement result and known to quantum state imaginary part information, structure is measured base;

Step 4, according to the measurement base described in step 3, each auxiliary sender measures the particle that it has, and the measurement result of described particle is sent to recipient;

Step 5, recipient receives core sender and 1 auxiliary sender's of N – measurement result, choose unitary operator, the core sender that recipient is received and 1 auxiliary sender's of N – measurement result, the particle that recipient is had carries out operation at the tenth of the twelve Earthly Branches, obtains the quantum state of required preparation | φ >.

2. a kind of full probability according to claim 1 long-range combined preparation process of quantum state in many ways arbitrarily, is characterized in that, in step 1, described real part is measured base by 2 ⁿindividual quadrature quantum state forms, and its mathematical form is

${\left\{{(-1)}^{i_1}a\right|i_1{i}_2...i_N\&rang;}_{A_1,A_2,...,A_N}+{b|\stackrel{\&OverBar;}{i_1{i}_2}...\stackrel{\&OverBar;}{i_N}\&rang;}_{A_1,A_2,...,A_N}|i_k\&Element;\{\mathrm{0,1}\},\stackrel{\&OverBar;}{i_k}=1-i_k,1\&le;k\&le;N\}.$

3. a kind of full probability according to claim 1 long-range combined preparation process of quantum state in many ways arbitrarily, is characterized in that, in step 3, described measurement base table is shown:

Wherein: l _jfor the j position of core sender measurement result,

be j the part imaginary part information known to auxiliary sender, and

4. a kind of full probability according to claim 1 long-range combined preparation process of quantum state in many ways arbitrarily, is characterized in that, in step 5, described operation at the tenth of the twelve Earthly Branches refers to: from I, and Z, X, ZX} chooses a kind of operation in operation tetra-tenth of the twelve Earthly Branches; This operation at tenth of the twelve Earthly Branches

be expressed as follows:

Wherein,

I=|0><0|+|1>LEs sT.LTssT.LT1|, Z=|0><0|-|1>LEs sT.LTssT.LT1|, X=|0><1|+|1>LEs sT.LTssT.LT0|; l _jfor the j position of core sender measurement result, m ₁, m ₂, m _j..., m _n-1the measurement result that represents respectively N-1 auxiliary sender, and m _j{ 0,1}, ⊕ represents binary system xor operation to ∈.

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