Research On The Key Theory Of Quantum State Private Transmission

The emergence of quantum computer threatens the widely used classical private communication system,so researchers turn their attention to quantum private communication.Compared with the classical private communication,the quantum private communication only relies on the related principles of quantum mechanics,and has the advantages of unconditional security,efficient information processing and large capacity of information transmission,providing more effective technical guarantee for the secure information transmission.In quantum private communication,quantum state,as the carrier of quantum information,can carry more abundant information and make the information transmission and processing more efficient and secure.Therefore,the quantum state private transmission theory attracts the attention of a large number of domestic and foreign researchers,and is a hot research topic in the field of quantum communication.On the one hand,the secure transmission of quantum information is realized by using quantum entanglement resources and classical communication.The key to optimize the quantum state private transmission is to select and construct a suitable quantum entanglement resource and measurement basis.On the other hand,quantum homomorphic encryption provides the ability to perform operations on encrypted information without decryption during the quantum state private transmission.The aim of improving the ability of quantum state operation in private transmission is to design a quantum homomorphic encryption scheme based on quantum state sharing.These key theories have laid the foundation for the safe,efficient and large-scale transmission of quantum information and promoted the development of quantum private communication.In this thesis,firstly,the controlled bidirectional private transmission of quantum states is studied.By constructing appropriate quantum entanglement resources and measurement basis,optimized schemes of quantum state symmetric,asymmetric and universal controlled bidirectional private transmission are proposed to complete efficient quantum information transmission and reduce classical communication cost.It solves the problems,such as the small number of quantum state particles,the need for auxiliary resources,the large cost of classical communication and the low efficiency of the scheme,in the current quantum state bidirectional private transmission schemes.Secondly,this thesis proposes a quantum homomorphic encryption scheme based on(k,n)threshold quantum state sharing.In the process of quantum state private transmission,any d(k?d?n,n?2)evaluators can complete homomorphic evaluation operation on encrypted quantum state sequences.It solves the problem that the number of evaluators in the current quantum homomoiphic encryption schemes can only be 1 or n,which lack flexibility.The research results and innovations of this thesis are as follows:(1)Three symmetric controlled bidirectional private transmission schemes of single-,two-and three-qubit states are proposed,and five-,nine-and thirteen-qubit entangled states are selected as quantum channels respectively.Firstly,in the ideal environment,the real and complex coefficients of quantum state are considered,and the corresponding measurement basis is constructed.Secondly,the effect of noise on the scheme is studied,including bit-flip,phase-flip,amplitude-damping,phase-damping and depolarizing noisy environments.Through comparison,it can be seen that the scheme realizes the bidirectional private transmission of multi-particle state,improves the communication efficiency,optimizes the classical communication consumption,and ensures the secure and rapid transmission of quantum information.(2)Two asymmetric schemes are proposed to realize controlled bidirectional private transmission of single-and three-qubit,two-and three-qubit equatorial state respectively by using nine-and eleven-qubit entangled states as quantum channels.According to the measurement results and the corresponding recovery operations,the receiver can recover the transmitted equatorial states deterministically.The effects of noisy environment on the schemes are described by calculating fidelities of the output states.Since no auxiliary resources are introduced in the scheme,the communication costs are reduced,the multi-particle equatorial states bidirectional transmission can be completed,and the communication efficiency is improved.(3)A universal scheme of controlled bidirectional private transmission n1-and n2-qubit equatorial states is presented,where n1,n2 are arbitrary non-zero positive integers.As we know,it is the first time to realize the bidirectional transmission of any particle equatorial state.Participants share the(2n1+2n2+1)-qubit entangled states as quantum channel.Using appropriate measurement basis and recovery operations,equatorial states can be transmitted simultaneously,safely and deterministically.With two different values of n1,n2,two specific examples of the universal scheme are given,namely symmetric and asymmetric equatorial state bidirectional transmission schemes.Finally,the two schemes are compared with the existing symmetric and asymmetric schemes.(4)The problem of homomorphic operation on encrypted quantum information during quantum state private transmission is further studied.Based on a(k,n)threshold quantum state sharing,a novel quantum homomorphic encryption scheme is proposed.The number of evaluators is flexible.Without decrypting the encrypted quantum state sequences,any d(k?d?n)evaluators are allowed to complete the evaluation of single-qubit unitary operations on the shared encrypted sequences,n?2,any subset of less than k evaluators neither can obtain the encrypted sequences being operated,nor the evaluation be completed.Next,for n=1,a quantum homomorphic encryption scheme are also given.Finally,the security of the scheme is analyzed,including the security of the private key,the plaintext sequence and the encrypted sequence.The implementation of the scheme requires less resources,and the number of evaluators is d(k?d?n).Therefore,the scheme is flexible,which provides a more optimized theoretical basis for the research on the quantum information private transmission and processing,and plays an important role in promoting the development of quantum private communication.