CN103368658A

CN103368658A - Four-photon entangled W state-based super-dense coding method for quantum signaling

Info

Publication number: CN103368658A
Application number: CN201310280566XA
Authority: CN
Inventors: 聂敏; 刘晓慧; 曹亚梅; 张美玲; 梁彦霞
Original assignee: Xian University of Posts and Telecommunications
Current assignee: Shaanxi Optoelectronic Integrated Circuit Pilot Technology Research Institute Co ltd
Priority date: 2013-07-05
Filing date: 2013-07-05
Publication date: 2013-10-23
Anticipated expiration: 2033-07-05
Also published as: CN103368658B

Abstract

The invention discloses a quantum signaling ultra-dense coding method based on four-photon entangled W state, which mainly solves the problems of small signaling coding capacity, low efficiency and low security in the quantum communication process. The implementation process is that the sender prepares four photons (A, B, C, D) entangled W state |Φ> _ABCD to represent quantum signaling, and sends photons C and D to the receiver; Unitary transformation, get 16 new quantum states |Φ _m >_A′B′CD; use these 16 new quantum states |Φ _m > _A′B′CD to form an orthogonal basis {|Φ _m > _A′B′CD }; Encode each new quantum state |Φ _m > _A′B′CD separately, and send the photons A′ and B′ obtained by unitary transformation to the receiver in sequence; the receiver receives photons A′ and After B′, randomly select a measurement basis from the orthogonal basis {|Φ _m > _A′B′CD }, conduct joint measurement on photons A′, B′, C, and D, measure the new quantum state, and complete the decoding . The invention has the advantages of high coding efficiency, large capacity and good security, and can be used in a signaling system of quantum mobile communication.

Description

An ultra-dense encoding method for quantum signaling based on four-photon entangled W states

技术领域technical field

本发明属于编码技术领域，特别是一种量子信令超密编码的方法，可用于量子通信网络。The invention belongs to the technical field of encoding, in particular to a quantum signaling ultra-dense encoding method, which can be used in quantum communication networks.

背景技术Background technique

信令是任何通信系统必不可少的重要组成部分，量子通信也不例外。在多用户量子通信网络中，量子信令的编码方式直接影响着信令系统的传输效率和安全性。Signaling is an essential and important part of any communication system, and quantum communication is no exception. In a multi-user quantum communication network, the encoding method of quantum signaling directly affects the transmission efficiency and security of the signaling system.

现有的量子编码方案主要有振幅编码，频率编码，相位编码，差分相位编码，以及两光子纠缠超密编码、三光子纠缠受控超密编码和四光子纠缠受控超密编码。其中：Existing quantum coding schemes mainly include amplitude coding, frequency coding, phase coding, differential phase coding, and two-photon entanglement ultra-dense coding, three-photon entanglement controlled ultra-dense coding and four-photon entanglement controlled ultra-dense coding. in:

振幅编码、频率编码、相位编码以及差分相位编码的编码效率比较低，一次编码只能传输1比特的信息。The encoding efficiency of amplitude encoding, frequency encoding, phase encoding and differential phase encoding is relatively low, and only one bit of information can be transmitted in one encoding.

两光子纠缠超密编码，一次编码就可以传输2比特的经典信息，但是，在多用户之间进行通信的过程中，信令系统的容量比较大，这种编码方式需要进行多次编码，才能够满足通信要求，比较繁琐；Two-photon entanglement ultra-dense coding, one coding can transmit 2 bits of classical information, however, in the process of communication between multiple users, the capacity of the signaling system is relatively large, this coding method needs to be coded multiple times to achieve It can meet the communication requirements and is relatively cumbersome;

三光子纠缠受控超密编码，除了接收方和发送方，还需要一个控制方，并且编码效率主要和控制方对自己的光子进行冯诺依曼测量时的测量角度有关，因为角度的限制，所以一次编码传输的经典信息小于3比特，并且编码过程特别繁琐，编码效率比较低；Three-photon entanglement controlled ultra-dense coding requires a controller in addition to the receiver and sender, and the coding efficiency is mainly related to the measurement angle when the controller performs von Neumann measurements on its own photons. Because of the limitation of the angle, Therefore, the classic information transmitted by one encoding is less than 3 bits, and the encoding process is particularly cumbersome, and the encoding efficiency is relatively low;

四光子纠缠受控超密编码，除了接收方和发送方，还存在两个控制方，同三光子一样，编码效率主要和控制方对自己的光子进行冯诺依曼测量时的测量角度有关，因为角度的限制，四光子纠缠受控超密编码的编码效率小于4比特，相比于三光子，编码容量有所提高，但是，编码效率基本不变。Four-photon entanglement controlled ultra-dense coding, in addition to the receiver and the sender, there are two controllers, like the three-photon, the coding efficiency is mainly related to the measurement angle when the controller performs von Neumann measurement on its own photons, Due to the limitation of the angle, the coding efficiency of the four-photon entanglement controlled ultra-dense coding is less than 4 bits. Compared with the three-photon coding, the coding capacity is improved, but the coding efficiency is basically unchanged.

发明内容Contents of the invention

本发明的目的在于针对上述四光子纠缠受控超密编码方法的不足，提出一种基于四光子纠缠W态的量子信令超密编码方法，以提高一次编码的容量和效率。The object of the present invention is to address the shortcomings of the above-mentioned four-photon entanglement controlled ultra-dense encoding method, and propose a quantum signaling ultra-dense encoding method based on four-photon entanglement W state, so as to improve the capacity and efficiency of one-time encoding.

实现本发明的技术思路是，利用四光子纠缠W态表示量子信令，直接建立了纠缠信道，并根据所要传输的经典信息对四光子纠缠态进行相应的幺正变换，得到新的量子态，再对新量子态进行编码。具体步骤如下：The technical idea of realizing the present invention is to use the four-photon entangled W state to represent quantum signaling, directly establish an entanglement channel, and perform corresponding unitary transformations on the four-photon entangled state according to the classical information to be transmitted to obtain a new quantum state. Then encode the new quantum state. Specific steps are as follows:

（1）发送方Alice利用紫外脉冲光连续通过两个偏硼酸钡晶体，产生由第一光子A、第二光子B、第三光子C、第四光子D这四个光子纠缠的W态|Φ>_ABCD，作为量子信令，并将第三光子C和第四光子D通过信道分发给接收方Bob，这样发送方Alice和接收方Bob就共享了W态|Φ>_ABCD；(1) Alice, the sender, uses ultraviolet pulsed light to continuously pass through two barium metaborate crystals to generate a W state entangled by four photons: the first photon A, the second photon B, the third photon C, and the fourth photon D |Φ > _ABCD , as quantum signaling, and distribute the third photon C and the fourth photon D to the receiver Bob through the channel, so that the sender Alice and the receiver Bob share the W state |Φ>_ABCD;

（2）发送方Alice对自己拥有的第一光子A和第二光子B进行幺正变换，以完成编码，得到新的量子态|Φ_m>_A′B′CD，其中A′和B′是光子A和光子B经过幺正幺正变换得到的光子，m={1,2,3,4,5,6,7,8，9,10,11,12,13,14,15,16}；(2) Alice, the sender, performs unitary transformation on the first photon A and the second photon B owned by herself to complete the encoding and obtain a new quantum state |Φ _m > _A′B′CD , where A′ and B′ are Photons obtained by unitary unitary transformation of photon A and photon B, m={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} ;

（3）发送方Alice完成编码后，把经过幺正幺正变换得到的光子A′和B′进行顺序重排，以A′B′或者B′A′的顺序，通过信道发送给接收方Bob；(3) After Alice, the sender, completes the encoding, she rearranges the order of the photons A' and B' obtained through the unitary unitary transformation, and sends them to the receiver Bob through the channel in the order of A'B' or B'A' ;

（4）接收方Bob收到光子A′和B′后选择测量基，对所述的四个光子A′、B′、C、D进行联合测量，测得新的量子态|Φ_m>_A′B′CD，以完成解码，得到Alice传输的经典信令信息。(4) Receiver Bob selects the measurement base after receiving photons A′ and B′, and performs joint measurement on the four photons A′, B′, C, and D, and obtains a new quantum state |Φ _m > _{A 'B'CD} to complete the decoding and obtain the classic signaling information transmitted by Alice.

本发明具有如下优点：The present invention has the following advantages:

1.本发明由于采用四光子纠缠W态表示量子信令，可直接建立纠缠信道，节省了信道资源，提高了通信效率；1. Since the present invention uses four-photon entanglement W state to represent quantum signaling, entanglement channels can be directly established, channel resources are saved, and communication efficiency is improved;

2.本发明由于通过对信令的量子态进行幺正变换，提高了编码容量，使一次编码能传输4比特经典信令信息；2. The present invention improves the encoding capacity by carrying out unitary transformation to the quantum state of the signaling, so that one encoding can transmit 4 bits of classical signaling information;

3．本发明在编码过程中，发送方Alice只传输两个光子，就可以实现传输4比特的经典信令信息，所以编码效率高；3. In the encoding process of the present invention, the sender Alice only transmits two photons, and can realize the transmission of 4-bit classical signaling information, so the encoding efficiency is high;

4．发送方Alice在编码完成后，把幺正变换后得到的光子发送到接收方Bob时，对每一个光子的发送顺序进行重新排列，这样提高了编码的安全性，保证了量子通信的顺利进行。4. Alice, the sender, rearranges the sending order of each photon when sending the photons obtained after the unitary transformation to Bob after the encoding is completed, which improves the security of the encoding and ensures the smooth progress of quantum communication.

附图说明Description of drawings

图1本发明量子信令编码流程图Figure 1 Quantum signaling coding flow chart of the present invention

图2是本发明进行量子信令的传输图。Fig. 2 is a transmission diagram of quantum signaling in the present invention.

图3本发明中的量子信令编码格式图；Quantum signaling coding format diagram among Fig. 3 the present invention;

具体实施方式Detailed ways

参照图1，本发明的具体实现步骤如下：With reference to Fig. 1, the concrete realization steps of the present invention are as follows:

步骤1，四光子纠缠对的制备和分发；Step 1, preparation and distribution of four-photon entangled pairs;

1.1）Alice作为信令发送方，利用紫外脉冲光连续通过两个偏硼酸钡晶体，制备有序的n个四光子A_k,B_k,C_k,D_k的纠缠W态

1.1) Alice, as the signaling sender, uses ultraviolet pulsed light to continuously pass through two barium metaborate crystals to prepare n four-photon entangled W states of A _k , B _k , C _k , and D _k

$| | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 00010001 > > + + \frac{11}{22} | | 00100010 > > + + \frac{11}{22} | | 01000100 > > + + \frac{11}{22} | | 10001000 > >,,$

其中，k=1,2,3,4,…，n,n≥1，0表示光子自旋方向为水平状态，1表示光子自旋方向为垂直状态；Among them, k=1, 2, 3, 4,..., n, n≥1, 0 means that the photon spin direction is in a horizontal state, and 1 means that the photon spin direction is in a vertical state;

1.2）Alice将光子C_k和D_k组成序列Q_B={C_k,D_k}，发给接收方Bob，自己保存光子A_k和B_k组成的序列Q_A={A_k，B_k}，1.2) Alice sends photons C _k and D _k to form a sequence Q _B = {C _k , D _k }, sends it to the receiver Bob, and saves the sequence Q _A = {A _k , B _k } composed of photons A _k and B _k ,

如图2所示，Alice将光子序列Q_B={C_k,D_k}通过量子信道传送至量子交换机A，量子交换机A根据接收方Bob所在的交换中心地址，再把光子序列Q_B={C_k,D_k}通过量子信道传送至该交换中心的量子交换机B，量子交换机B根据Bob的目的地址，选择合适的路由，再把光子序列Q_B={C_k,D_k}传送给Bob；As shown in Figure 2, Alice transmits the photon sequence Q _B ={C _k ,D _k } to the quantum switch A through the quantum channel, and the quantum switch A sends the photon sequence Q _B ={ C _k , D _k } are transmitted to the quantum switch B of the switching center through the quantum channel, and the quantum switch B selects an appropriate route according to Bob's destination address, and then transmits the photon sequence Q _B ={C _k ,D _k } to Bob ;

1.3）当Bob收到序列Q_B后，发送方Alice与接收方Bob建立纠缠信道，双方共享四光子W态

1.3) When Bob receives the sequence Q _B , the sender Alice establishes an entanglement channel with the receiver Bob, and both parties share the four-photon W state

步骤2，Alice将四光子纠缠W态

作为量子信令，并对光子A_k和B_k进行幺正变换，以完成对量子信令的编码。Step 2, Alice entangles four photons in W state

As quantum signaling, and unitary transformation is performed on photons A _k and B _k to complete the encoding of quantum signaling.

如图3所示，量子信令编码的格式是由信令单元组成的，信令单元是信令消息的最小单元,长度为8比特，对量子信令进行两次编码就可以实现。As shown in Figure 3, the format of quantum signaling encoding is composed of signaling units. The signaling unit is the smallest unit of a signaling message, with a length of 8 bits, which can be realized by encoding quantum signaling twice.

2.1）发送方Alice根据要传输的经典信令消息，从幺正算子集合中选取一个对应的幺正算子；2.1) The sender Alice selects a corresponding unitary operator from the set of unitary operators according to the classic signaling message to be transmitted;

幺正算子集合为：{U₀,U₁,U₂,U₃,U₄,U₅,U₆,U₇,U₈,U₉,U₁₀,U₁₁,U₁₂,U₁₃,U₁₄,U₁₅}，算子集合中的每个元素都是16维的矩阵，每个矩阵分别表示为：The set of unitary operators is: {U ₀ , U ₁ , U ₂ , U ₃ , U ₄ , U ₅ , U ₆ , U ₇ , U ₈ , U ₉ , U 10 , U ₁₁ , U ₁₂ , _{U 13} _, U ₁₄ , U ₁₅ }, each element in the operator set is a 16-dimensional matrix, and each matrix is expressed as:

${U u}_{00} = = {δ δ}_{00} &CircleTimes; &CircleTimes; {δ δ}_{00} &CircleTimes; &CircleTimes; {δ δ}_{00} &CircleTimes; &CircleTimes; {δ δ}_{00},, {U u}_{11} = = {δ δ}_{33} &CircleTimes; &CircleTimes; {δ δ}_{33} &CircleTimes; &CircleTimes; {δ δ}_{00} &CircleTimes; &CircleTimes; {δ δ}_{00},, {U u}_{22} = = {δ δ}_{11} &CircleTimes; &CircleTimes; {δ δ}_{00} &CircleTimes; &CircleTimes; {δ δ}_{00} &CircleTimes; &CircleTimes; {δ δ}_{00},,$

${U u}_{33} = = {- - iδ iδ}_{22} &CircleTimes; &CircleTimes; {δ δ}_{33} &CircleTimes; &CircleTimes; {δ δ}_{00} &CircleTimes; &CircleTimes; {δ δ}_{00},, {U u}_{44} = = {δ δ}_{11} &CircleTimes; &CircleTimes; {δ δ}_{11} &CircleTimes; &CircleTimes; {δ δ}_{11} &CircleTimes; &CircleTimes; {δ δ}_{11},, {U u}_{55} = = {- - δ δ}_{22} &CircleTimes; &CircleTimes; {δ δ}_{22} &CircleTimes; &CircleTimes; {δ δ}_{11} &CircleTimes; &CircleTimes; {δ δ}_{11},,$

${U u}_{66} = = {δ δ}_{00} &CircleTimes; &CircleTimes; {δ δ}_{11} &CircleTimes; &CircleTimes; {δ δ}_{11} &CircleTimes; &CircleTimes; {δ δ}_{11},, {U u}_{77} = = {δ δ}_{00} &CircleTimes; &CircleTimes; {δ δ}_{11} &CircleTimes; &CircleTimes; {δ δ}_{22} &CircleTimes; &CircleTimes; {δ δ}_{22},, {U u}_{88} = = {δ δ}_{00} &CircleTimes; &CircleTimes; {δ δ}_{33} &CircleTimes; &CircleTimes; {δ δ}_{11} &CircleTimes; &CircleTimes; {δ δ}_{22},,$

${U u}_{1212} = = {- - δ δ}_{11} &CircleTimes; &CircleTimes; {iδ iδ}_{22} &CircleTimes; &CircleTimes; {δ δ}_{00} &CircleTimes; &CircleTimes; {δ δ}_{33},, {U u}_{1313} = = {- - δ δ}_{11} &CircleTimes; &CircleTimes; {iδ iδ}_{22} &CircleTimes; &CircleTimes; {δ δ}_{33} &CircleTimes; &CircleTimes; {δ δ}_{00},, {U u}_{1414} = = {δ δ}_{00} &CircleTimes; &CircleTimes; {iδ iδ}_{22} &CircleTimes; &CircleTimes; {δ δ}_{00} &CircleTimes; &CircleTimes; {δ δ}_{33},,$

${U u}_{1515} = = {δ δ}_{00} &CircleTimes; &CircleTimes; {- - iδ iδ}_{22} &CircleTimes; &CircleTimes; {δ δ}_{33} &CircleTimes; &CircleTimes; {δ δ}_{00};;$

其中，i表示虚数，

表示张量积，δ₀,δ₁,δ₂,δ₃为Pauli矩阵,

δ_{0} = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}],

δ_{1} = [\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}], δ_{2} = [\begin{matrix} 0 & - i \\ i & 0 \end{matrix}], δ_{3} = [\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}];

Among them, i represents an imaginary number,

Indicates tensor product, δ ₀ , δ ₁ , δ ₂ , δ ₃ are Pauli matrices,

δ_{0} = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}],

δ_{1} = [\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}], δ_{2} = [\begin{matrix} 0 & - i \\ i & 0 \end{matrix}], δ_{3} = [\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}];

2.2）Alice选取算子后，对光子A_k和B_k进行幺正变换，得到新量子态

其中，A′_k和B_′k是光子A_k和光子B_k经过幺正变换得到的光子，m={1,2,3,4,5,6,7,8，9,10,11,12,13,14,15,16}，每个新量子态

的量子表示式为：2.2) After Alice selects the operator, she performs unitary transformation on the photons A _k and B _k to obtain a new quantum state

Among them, A′ _k and B _′ k are photons obtained by unitary transformation of photon A _k and photon B _k , m={1,2,3,4,5,6,7,8,9,10,11, 12,13,14,15,16}, each new quantum state

The quantum expression of is:

$| | {Φ Φ}_{11} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{00} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 00010001 > > + + \frac{11}{22} | | 00100010 > > + + \frac{11}{22} | | 01000100 > > + + \frac{11}{22} | | 10001000 > >,,$

$| | {Φ Φ}_{22} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{11} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 00010001 > > + + \frac{11}{22} | | 00100010 > > - - \frac{11}{22} | | 01000100 > > - - \frac{11}{22} | | 10001000 > >,,$

$| | {Φ Φ}_{33} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{22} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 10011001 > > + + \frac{11}{22} | | 10101010 > > + + \frac{11}{22} | | 11001100 > > + + \frac{11}{22} | | 00000000 > >,,$

$| | {Φ Φ}_{44} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{33} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 10011001 > > + + \frac{11}{22} | | 10101010 > > - - \frac{11}{22} | | 11001100 > > - - \frac{11}{22} | | 00000000 > >,,$

$| | {Φ Φ}_{55} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{44} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 11101110 > > + + \frac{11}{22} | | 11011101 > > + + \frac{11}{22} | | 10111011 > > + + \frac{11}{22} | | 01110111 > >,,$

$| | {Φ Φ}_{66} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{55} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 11101110 > > + + \frac{11}{22} | | 11011101 > > - - \frac{11}{22} | | 10111011 > > - - \frac{11}{22} | | 01110111 > >,,$

$| | {Φ Φ}_{77} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{66} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 01100110 > > + + \frac{11}{22} | | 01010101 > > + + \frac{11}{22} | | 00110011 > > + + \frac{11}{22} | | 11111111 > >,,$

$| | {Φ Φ}_{88} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{77} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 01100110 > > + + \frac{11}{22} | | 01010101 > > - - \frac{11}{22} | | 00110011 > > - - \frac{11}{22} | | 11111111 > >,,$

$| | {Φ Φ}_{99} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{88} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 00100010 > > - - \frac{11}{22} | | 00010001 > > + + \frac{11}{22} | | 01110111 > > - - \frac{11}{22} | | 10111011 > >,,$

$| | {Φ Φ}_{1010} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{99} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 00100010 > > - - \frac{11}{22} | | 00010001 > > - - \frac{11}{22} | | 01110111 > > + + \frac{11}{22} | | 10111011 > >,,$

$| | {Φ Φ}_{1111} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{1010} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 10011001 > > + + \frac{11}{22} | | 00110011 > > - - \frac{11}{22} | | 10101010 > > - - \frac{11}{22} | | 11111111 > >,,$

$| | {Φ Φ}_{1212} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{1111} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 10011001 > > - - \frac{11}{22} | | 00110011 > > - - \frac{11}{22} | | 10101010 > > + + \frac{11}{22} | | 11111111 > >,,$

$| | {Φ Φ}_{1313} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{1212} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 01000100 > > - - \frac{11}{22} | | 10001000 > > - - \frac{11}{22} | | 11011101 > > + + \frac{11}{22} | | 11101110 > >,,$

$| | {Φ Φ}_{1414} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{1313} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 01000100 > > - - \frac{11}{22} | | 10001000 > > + + \frac{11}{22} | | 11011101 > > - - \frac{11}{22} | | 11101110 > >,,$

$| | {Φ Φ}_{1515} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{1414} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 01010101 > > + + \frac{11}{22} | | 00000000 > > - - \frac{11}{22} | | 01100110 > > - - \frac{11}{22} | | 11001100 > >,,$

$| | {Φ Φ}_{1616} {> >}_{{A A}_{k k}^{' '} {B B}_{k k}^{' '} {C C}_{k k} {D D.}_{k k}} = = {U u}_{1515} | | Φ Φ {> >}_{{A A}_{k k} {B B}_{k k} {C C}_{k k} {D D.}_{k k}} = = \frac{11}{22} | | 01010101 > > - - \frac{11}{22} | | 00000000 > > - - \frac{11}{22} | | 01100110 > > + + \frac{11}{22} | | 11001100 > >,,$

上述这16种新的量子态构成一个完备正交基

新的量子态

满足关系式：The above 16 new quantum states constitute a complete orthogonal basis

new quantum state

satisfy the relation:

$\{\begin{matrix} < < {Φ Φ}_{m m} | | {Φ Φ}_{j j} > > = = {δ δ}_{mj mj} \\ \underset{m m}{Σ Σ} \underset{j j}{Σ Σ} < < {Φ Φ}_{m m} | | {Φ Φ}_{j j} > > = = I I \end{matrix}$

其中，<Φ_m|Φ_j>表示量子态

和

的内积，

δ_{ij} = \{\begin{matrix} 1, i = j \\ 0, i &NotEqual; j \end{matrix},

I = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}],

m,j∈[1,16]；where, <Φ _m |Φ _j > represents the quantum state

and

inner product of

δ_{ij} = \{\begin{matrix} 1, i = j \\ 0, i &NotEqual; j \end{matrix},

I = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}],

m,j∈[1,16];

2.3）Alice对得到的每个新量子态

分别进行编码，即将2.3) Alice pairs each new quantum state obtained

Encoded separately, the upcoming

编码为0000， coded as 0000,

编码为0001，

Coded as 0001,

编码为0010，

Coded as 0010,

编码为0101，

Coded as 0101,

编码为0100，

Coded as 0100,

编码为0101，

Coded as 0101,

编码为0110，

Coded as 0110,

编码为0111，

Coded as 0111,

编码为1000，

encoded as 1000,

编码为1001， Coded as 1001,

编码为1010， Coded as 1010,

编码为1011，

Coded as 1011,

编码为1100，

Coded as 1100,

编码为1101，

Coded as 1101,

编码为1110，

Coded as 1110,

编码为1111。

The code is 1111.

步骤3，发送方Alice将光子序列发送给接收方Bob。Step 3, the sender Alice sends the photon sequence to the receiver Bob.

3.1）编码完成后，Alice把幺正变换后得到的光子A_k′和光子B_k′组成光子序列Q_A′={A₁′，B₁′，A₂′，B₂′…A_k′，B_k′…A_n′，B_n′}；3.1) After the encoding is completed, Alice forms the photon sequence Q _A ′={A ₁ ′, B ₁ ′, A ₂ ′, B ₂ ′…A _k ′ with the photon A _k ′ and photon B _k ′ obtained after the unitary transformation , B _k ′… A _n ′, B _n ′};

3.2）Alice对光子序列Q_A′={A₁′，B₁′，A₂′，B₂′…A_k′，B_k′…A_n′，B_n′}里面的所有光子，按先排列B_k′，后排列A_k′的顺序进行重新排列，得到新的光子序列Q_A′′；3.2) For all photons in the photon sequence Q _A ′={A ₁ ′, B ₁ ′, A ₂ ′, B ₂ ′…A _k ′, B _k ′…A _n ′, B _n ′}, Alice presses first Arrange B _k ′, then rearrange the order of A _k ′ to obtain a new photon sequence Q _A ′′;

3.3）Alice把新的光子序列Q_A′′通过量子信道发送给接收方Bob，并通过经典信道告知Bob光子A_k′和光子B_k′在新的光子序列Q_A′′中的位置。3.3) Alice sends the new photon sequence Q _A ′′ to the receiver Bob through the quantum channel, and informs Bob of the positions of photon A _k ′ and photon B _k ′ in the new photon sequence Q _A ′′ through the classical channel.

步骤4，接收方Bob对接收到的量子信令进行解码。Step 4, the receiver Bob decodes the received quantum signaling.

4.1）接收方Bob收到新的光子序列Q_A′′后，把光子序列Q_A′′恢复到光子序列Q_A′={A₁′，B₁′，A₂′，B₂′…A_k′，B_k′…A_n′，B_n′}；4.1) After the receiver Bob receives the new photon sequence Q _A ′′, he restores the photon sequence Q _A ′′ to the photon sequence Q _A ′={A ₁ ′, B ₁ ′, A ₂ ′, B ₂ ′…A _k ', B _k '...A _n ', B _n '};

4.2）Bob从完备正交基中，选择其中的任意一种作为测量基；4.2) Bob starts from the complete orthogonal basis Among them, choose any one of them as the measurement base;

4.3）Bob利用测量基对所述的四个光子A_k′，B_k′，C_k，D_k进行联合测量，得到新量子态

完成解码，得到Alice发送的经典信令信息。4.3) Bob uses the measurement basis to jointly measure the four photons A _k ′, B _k ′, C _k , and D _k to obtain a new quantum state

Complete the decoding and get the classic signaling information sent by Alice.

结束语conclusion

以上描述仅是本发明的一个具体实例，不构成对本发明的任何限制，显然对于本领域的专业人员来说，在了解了本发明内容和原理后，都可能在不背离本发明原理、结构的情况下，进行形式和细节上的各种修改和改变，但是这些基于本发明思想的修正和改变仍在本发明的权利要求保护范围之内。The above description is only a specific example of the present invention, and does not constitute any limitation to the present invention. Obviously, for those skilled in the art, after understanding the content and principles of the present invention, it is possible without departing from the principles and structures of the present invention. In some cases, various modifications and changes in form and details are made, but these modifications and changes based on the idea of the present invention are still within the protection scope of the claims of the present invention.

Claims

1. A quantum signaling ultra-dense coding method based on four-photon entangled W state comprises the following steps:

(1) a sender Alice uses ultraviolet pulsed light to continuously pass through two barium metaborate crystals to generate a W state | phi which is entangled by four photons, namely a first photon A, a second photon B, a third photon C and a fourth photon D>_ABCDAs quantum signaling, and distributing the third photon C and the fourth photon D to the receiver Bob through the channel, so that the sender Alice and the receiver Bob share the W state | phi |>_ABCD；

(2) SendingThe party Alice performs unitary transformation on the first photon A and the second photon B owned by the party Alice to complete coding, and obtains a new quantum state | phi_m>_A′B′CDWherein, a 'and B' are photons obtained by performing unitary transformation on the photons a and B, and m = {1,2,3,4,5,6,7,8, 9,10,11,12,13,14,15,16 };

(3) after the sender Alice finishes coding, the photons A 'and B' obtained through the unitary-to-unitary conversion are sequentially rearranged and sent to a receiver Bob through a channel according to the sequence of A 'B' or B 'A';

(4) after receiving the photons A 'and B', the receiver Bob selects a measuring base, and performs combined measurement on the four photons A ', B' and C, D to obtain a new quantum state | phi_m>_A′B′CDTo complete decoding and obtain the classical signaling information transmitted by Alice.

2. The quantum signaling ultra-dense coding method based on four-photon entangled W state according to claim 1, wherein the four-photon entangled W state | Φ in the step (1)>_ABCDThe quantum state expression is as follows:

| Φ >_{A B C D} = \frac{1}{2} | 0001 > + \frac{1}{2} | 0010 > + \frac{1}{2} | 0100 > + \frac{1}{2} | 1000 >

where 0 indicates that the spin direction of the photon is the horizontal state and 1 indicates that the spin direction of the photon is the vertical state.

3. The quantum signaling super-dense coding method based on the four-photon entangled W state according to claim 1, wherein in the step (2), the sender Alice performs unitary transformation on the first photon A and the second photon B owned by itself, and the method comprises the following steps:

(2a) from unitary operator set { U₀,U₁,U₂,U₃,U₄,U₅,U₆,U₇,U₈,U₉,U₁₀,U₁₁,U₁₂,U₁₃,U₁₄,U₁₅Selecting a unitary operator, wherein each element in the operator set is a 16-dimensional matrix, and each matrix is represented as:

U_{0} = δ_{0} &CircleTimes; δ_{0} &CircleTimes; δ_{0} &CircleTimes; δ_{0}, U_{1} = δ_{3} &CircleTimes; δ_{3} &CircleTimes; δ_{0} &CircleTimes; δ_{0}, U_{2} = δ_{1} &CircleTimes; δ_{0} &CircleTimes; δ_{0} &CircleTimes; δ_{0},

U_{3} = {- iδ}_{2} &CircleTimes; δ_{3} &CircleTimes; δ_{0} &CircleTimes; δ_{0}, U_{4} = δ_{1} &CircleTimes; δ_{1} &CircleTimes; δ_{1} &CircleTimes; δ_{1}, U_{5} = {- δ}_{2} &CircleTimes; δ_{2} &CircleTimes; δ_{1} &CircleTimes; δ_{1},

U_{6} = δ_{0} &CircleTimes; δ_{1} &CircleTimes; δ_{1} &CircleTimes; δ_{1}, U_{7} = δ_{0} &CircleTimes; δ_{1} &CircleTimes; δ_{2} &CircleTimes; δ_{2}, U_{8} = δ_{0} &CircleTimes; δ_{3} &CircleTimes; δ_{1} &CircleTimes; δ_{2},

U_{12} = {- δ}_{1} &CircleTimes; {iδ}_{2} &CircleTimes; δ_{0} &CircleTimes; δ_{3}, U_{13} = {- δ}_{1} &CircleTimes; {iδ}_{2} &CircleTimes; δ_{3} &CircleTimes; δ_{0}, U_{14} = δ_{0} &CircleTimes; {iδ}_{2} &CircleTimes; δ_{0} &CircleTimes; δ_{3},

U_{15} = δ_{0} &CircleTimes; {- iδ}_{2} &CircleTimes; δ_{3} &CircleTimes; δ_{0};

wherein, i represents an imaginary number,

representing the tensor product, δ₀,δ₁,δ₂,δ₃In order to be a Pauli matrix,

δ_{0} = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}],

δ_{1} = [\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}], δ_{2} = [\begin{matrix} 0 & - i \\ i & 0 \end{matrix}], δ_{3} = [\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}];

(2b) after Alice selects a unitary operator, the quantum state | phi is subjected to>_ABCDPerforming unitary conversion to obtainTo a new quantum state | Φ_m>_A′B′CDEach new quantum state | Φ_m>_A′B′CDThe quantum representation of (a) is:

| Φ_{1} >_{A^{'} B^{'} CD} = U_{0} | Φ >_{ABCD} = \frac{1}{2} | 0001 > + \frac{1}{2} | 0010 > + \frac{1}{2} | 0100 > + \frac{1}{2} | 1000 >,

| Φ_{2} >_{A^{'} B^{'} CD} = U_{1} | Φ >_{ABCD} = \frac{1}{2} | 0001 > + \frac{1}{2} | 0010 > - \frac{1}{2} | 0100 > - \frac{1}{2} | 1000 >,

| Φ_{3} >_{A^{'} B^{'} CD} = U_{2} | Φ >_{ABCD} = \frac{1}{2} | 1001 > + \frac{1}{2} | 1010 > + \frac{1}{2} | 1100 > + \frac{1}{2} | 0000 >,

| Φ_{4} >_{A^{'} B^{'} CD} = U_{3} | Φ >_{ABCD} = \frac{1}{2} | 1001 > + \frac{1}{2} | 1010 > - \frac{1}{2} | 1100 > - \frac{1}{2} | 0000 >,

| Φ_{5} >_{A^{'} B^{'} CD} = U_{4} | Φ >_{ABCD} = \frac{1}{2} | 1110 > + \frac{1}{2} | 1101 > + \frac{1}{2} | 1011 > + \frac{1}{2} | 0111 >,

| Φ_{6} >_{A^{'} B^{'} CD} = U_{5} | Φ >_{ABCD} = \frac{1}{2} | 1110 > + \frac{1}{2} | 1101 > - \frac{1}{2} | 1011 > - \frac{1}{2} | 0111 >,

| Φ_{7} >_{A^{'} B^{'} CD} = U_{6} | Φ >_{ABCD} = \frac{1}{2} | 0110 > + \frac{1}{2} | 0101 > + \frac{1}{2} | 0011 > + \frac{1}{2} | 1111 >,

| Φ_{8} >_{A^{'} B^{'} CD} = U_{7} | Φ >_{ABCD} = \frac{1}{2} | 0110 > + \frac{1}{2} | 0101 > - \frac{1}{2} | 0011 > - \frac{1}{2} | 1111 >,

| Φ_{9} >_{A^{'} B^{'} CD} = U_{8} | Φ >_{ABCD} = \frac{1}{2} | 0010 > - \frac{1}{2} | 0001 > + \frac{1}{2} | 0111 > - \frac{1}{2} | 1011 >,

| Φ_{10} >_{A^{'} B^{'} CD} = U_{9} | Φ >_{ABCD} = \frac{1}{2} | 0010 > - \frac{1}{2} | 0001 > - \frac{1}{2} | 0111 > + \frac{1}{2} | 1011 >,

| Φ_{11} >_{A^{'} B^{'} CD} = U_{10} | Φ >_{ABCD} = \frac{1}{2} | 1001 > + \frac{1}{2} | 0011 > - \frac{1}{2} | 1010 > - \frac{1}{2} | 1111 >,

| Φ_{12} >_{A^{'} B^{'} CD} = U_{11} | Φ >_{ABCD} = \frac{1}{2} | 1001 > - \frac{1}{2} | 0011 > - \frac{1}{2} | 1010 > + \frac{1}{2} | 1111 >,

| Φ_{13} >_{A^{'} B^{'} CD} = U_{12} | Φ >_{ABCD} = \frac{1}{2} | 0100 > - \frac{1}{2} | 1000 > - \frac{1}{2} | 1101 > + \frac{1}{2} | 1110 >,

| Φ_{14} >_{A^{'} B^{'} CD} = U_{13} | Φ >_{ABCD} = \frac{1}{2} | 0100 > - \frac{1}{2} | 1000 > + \frac{1}{2} | 1101 > - \frac{1}{2} | 1110 >,

| Φ_{15} >_{A^{'} B^{'} CD} = U_{14} | Φ >_{ABCD} = \frac{1}{2} | 0100 > + \frac{1}{2} | 0000 > - \frac{1}{2} | 0110 > - \frac{1}{2} | 1100 >,

| Φ_{16} >_{A^{'} B^{'} CD} = U_{15} | Φ >_{ABCD} = \frac{1}{2} | 0101 > - \frac{1}{2} | 0000 > - \frac{1}{2} | 0110 > + \frac{1}{2} | 1100 >,

the 16 quantum states form a complete orthogonal basis phi_m>_A′B′CD}，|Φ_m>_A′B′CDSatisfy the relation:

\{\begin{matrix} < Φ_{m} | Φ_{j} > = δ_{mj} \\ \underset{m}{Σ} \underset{j}{Σ} < Φ_{m} | Φ_{j} > = I \end{matrix}

wherein,<Φ_m|Φ_j>representing a quantum state | Φ_m>_A′B′CDAnd | Φ_j>_A′B′CDThe inner product of (a) is,

δ_{ij} = \{\begin{matrix} 1, i = j \\ 0, i &NotEqual; j \end{matrix},

I = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}],

m,j∈[1,16]；

(2c) alice pairs each new quantum state | Φ_m>_A′B′CDAre coded separately, i.e. about

|Φ₁>_A′B′CDThe code is a code of 0000 and the code is a code of 0000,

|Φ₂>_A′B′CDthe code is a code of 0001 and is a code of 0001,

|Φ₃>_A′B′CDthe code is 0010 and the code is,

|Φ₄>_A′B′CDthe code is 0101 and the code is,

|Φ₅>_A′B′CDthe code is 0100, and the code is,

|Φ₆>_A′B′CDthe code is 0101 and the code is,

|Φ₇>_A′B′CDthe code is 0110 and the code is,

|Φ₈>_A′B′CDthe code is 0111 and the code is,

|Φ₉>_A′B′CDthe code is a code of 1000 and the code is a code,

|Φ₁₀>_A′B′CDthe code is a code of 1001 and the code is,

|Φ₁₁>_A′B′CDthe code is a code of 1010, and the code is,

|Φ₁₂>_A′B′CDthe code is 1011 of the number of codes,

|Φ₁₃>_A′B′CDthe code is coded into a code of 1100,

|Φ₁₄>_A′B′CDthe code is 1101 and the code is provided with,

|Φ₁₅>_A′B′CDthe code is a code of 1110 (one-time code),

|Φ₁₆>_A′B′CDthe code is 1111.

4. The quantum signaling ultra-dense coding method based on the four-photon entangled W state according to claim 1, wherein the measurement basis in the step (4) is a complete orthogonal basis { | Φ { |)_m>_A′B′CDAny one of them.