Research On The Key Issues Of Quantum Network Coding Based On Entandled Resources

With the development of quantum information technology,the construction of quantum communication network has been widely concerned.It is of great strategic significance to develop quantum communication technology.Quantum communication has the security characteristics that traditional classical communication does not have,which can improve the security of quantum information transmission.As an information processing method in quantum communication,quantum network coding is of great significance to improve the quantum information transmission efficiency and the total network throughput,and solve the transmission congestion problem at the bottleneck channel.At present,the research of quantum network coding has been in the stage of rapid development,and the proposal of efficient and secure quantum network coding scheme has become an important research topic in quantum communication.Quantum entanglement is an important physical resource in quantum communication network.It plays an important role in quantum information processing,including quantum teleportation,quantum network coding and quantum homomorphic encryption.The entanglement between particles is used to realize the long-distance secure quantum communication.However,due to the quantum non-cloning theorem,quantum state cannot be cloned arbitrarily and accurately like classical bits.Therefore,without auxiliary resources,the design of coding and decoding methods can only achieve high fidelity quantum network coding,but can not achieve fidelity 1.Considering quantum entangled states as auxiliary resources,aiming at the problems of quantum state transmission loss and invalid communication,high-dimensional state transmission loss and low channel utilization,quantum multi-unicast communication,quantum evaluation bottleneck in the process of double quantum homomorphic encryption,the thesis presents quantum network coding without loss of information,highdimensional quantum network coding based on prediction mechanism,quantum multicast communication based on butterfly network and cross quantum homomorphic encryption based on quantum network coding.The main research results of this thesis are as follows:(1)Aiming at the quantum states probability transmission problem,the non-maximum entangled states are adopted to design the encoding and decoding strategy,and the quantum network coding without loss of information is proposed to realize the cross and perfect communication,and improves the success probability of quantum state communication.Firstly,two pairs of non maximally entangled states are pre shared between senders of the butterfly network.By adding auxiliary particles and local operations to the sender,the 2-pair quantum network coding without information loss are realized.Secondly,the 2-pair scheme without information loss is extended to quantum k-pair network,which solves the problem of k-pair quantum states loss for quantum network coding,and realizes the perfect multi-unicast communication of k-pair quantum states.In addition,in order to further ensure the effectiveness and security of quantum state transmission,a controlled quantum network coding without information loss is proposed,which realizes the effective and secure transmission of quantum states with the consent of the third party.Finally,the proposed scheme not only solves the problem of quantum state loss,but also avoids the invalid utilization of quantum and classical channels.At the same time,it also solves the transmission congestion problem of quantum information at bottleneck channel with classical resources,and improves the transmission efficiency.(2)Aiming at the problems of high-dimensional states loss and highdimensional states transmission congestion,the high-dimensional nomaximum entangled states are applied to study the high-dimensional quantum system,the high-dimensional quantum network coding based on prediction mechanism is proposed,which realizes the deterministic highdimensional quantum network coding and improves the high-dimensional states transmission efficiency.Firstly,based on the advantages of highdimensional quantum system,the high-dimensional non-maximally entangled state is used as the quantum channel,the high-dimensional local operation is designed,and the transmission of high-dimensional state without loss of information is proposed.Secondly,the high dimensional state lossless transmission is applied to the butterfly network,the highdimensional coding and decoding strategy is designed,the problem of transmission congestion of high-dimensional states at the bottleneck channel is solved,and the deterministic high-dimensional quantum network coding is realized.The scheme uses the Z-basis in the twodimensional Hilbert space to predict the transmission of high-dimensional states.When the prediction is successful,the deterministic transmission of high-dimensional states can be realized on the butterfly network;When the prediction fails,the high-dimensional local recovery operation is designed to ensure that the high-dimensional state will not be lost and avoid preparing high-dimensional state again.Finally,the quantum circuits implementation of high-dimensional quantum network based on prediction mechanism is designed.(3)Aiming at the multi-unicast communication problem in quantum network coding,the coding and decoding strategy is designed by using the maximum entangled state,and the quantum multicast communication scheme based on butterfly network is proposed.Firstly,the maximum entangled states are pre-shared between the adjacent quantum repeaters of the butterfly network.In order to establish the entanglement relationship between the corresponding senders and receivers,the connection and removal operations are designed by applying local operations and classical communication.Secondly,the auxiliary particles are added according to the multicast number k,the controlled-NOT(CNOT)gates are applied to generate the multi-particle entangled states.The Bell basis and special single particle basis are used to performe quantum measurements,and the multicast coding strategy is designed.Finally,under the joint action of classical and quantum channels,the multicast decoding strategy is designed to realize quantum k-pair multicast communication.This scheme solves the problem of k-pair quantum states transmission congestion by applying classical coding at the bottleneck channel of k-pair extended butterfly network,realizes k-pair quantum multicast communication,and improves the efficiency of quantum information transmission.(4)Aiming at the bottleneck problem of quantum evaluation in the process of double quantum homomorphic encryption,the cross quantum homomorphic encryption based on the butterfly network is studied by using the maximum entangled states.Firstly,using the maximum entangled states as the quantum auxiliary resources,the senders apply Bell basis measurements to encrypt the plaintext quantum states.The encryption and decryption algorithms are designed.Secondly,the encryption algorithm is used to generate ciphertext quantum states,and the evaluation bottleneck problem of ciphertext quantum states is solved by performing classical coding operations at bottleneck nodes.Finally,considering the universal quantum computing,the quantum evaluation circuit is designed for different quantum computing.According to the decryption key,the decryption algorithm is applied to obtain the evaluated plaintext quantum states.This scheme solves the bottleneck evaluation problem based on butterfly network,realizes cross and perfect quantum homomorphic encryption,and improves the evaluation efficiency.In addition,according to different quantum evaluation operators,different quantum circuits for cross quantum homomorphic evaluation are designed based on the butterfly network.