Research On Protocols Of Remote State Preparation And Quantum Key Distribution

With the rapid development of science and technology, human society has stepped into the network information era. Because of a great many of information security incidents, information security has attracted people’s widespread attention. Consequently, private communication technology, which aims at guaranteeing the security of information, turns into the focus of research. Quantum information technology brings a revolutionary impact on the classic private communication technology which is based on the classical cryptography theory, especially quantum algorithm has posed a serious threat to the current public key crypto-systems. While quantum private communication technology based on physical properties can compensate for the lack of classic private communication technology well. Quantum private communication, which combines the classic information theory and quantum mechanics, is able to achieve efficient and secure transmission of information with quantum states as an information carrier. The related research on this subject owns important theoretical value and broad application prospects.Quantum private communication covers quantum communication, quantum cryptography and other fields. In this dissertation, we focus on remote state preparation protocols in quantum secure communication and quantum key distribution protocols in quantum cryptography. For remote state preparation, we concentrate on networking multi-source unicast and multi-source multicast remote state preparation protocols. While for quantum key distribution, we pay attention to quantum key distribution protocols based on channel encryption. The innovation achievements of this dissertation are as follows:(1) For multi-source unicast remote state preparation, the remote state preparation is divided into four categories:single-source unicast, multi-source unicast, single-source multicast and multi-source multicast by reference to the classification method of network transport protocols and pointed out the advantages together with disadvantages of each type of protocols. We focus on the remote preparation for multi-particle entangled states, which is less studied in other references. We elaborate joint remote preparation schemes of an arbitrary five-qubit Brown state and controlled joint remote preparation schemes of an arbitrary four-qubit χ-state based on the maximally entangled channels and partially entangled channels. Utilizing maximally entangled channels, the efficiency of these two schemes is up to 100%, while partially entangled channels, we make use of a specific collective unitary operation and an optimal positive operator-valued measure to restore the desired states and compare the two methods by taking into account the number of auxiliary particles, the success probability of protocols and the dimensions of unitary operations. Compared with similar protocols, the efficiency of these two protocols in our dissertation is significantly increased. Furthermore, we study the maximally entangled channels and partially entangled channels and exploit two methods to deal with the partially entangled channels in these two schemes.(2) For multi-source multicast remote state preparation, we clarify common design techniques on four types of remote state preparation protocols and point out the key to devise such multi-source multicast remote state preparation protocols is how to construct some high dimensional basis transformation matrices. It is demonstrated that when the dimensions of matrices satisfy n>8, there are not some general real unitary basis transformation matrices with related theorems and corollaries. We construct a special kind of 16-dimensional real unitary basis transformation matrices and a very special kind of 16-dimensional complex unitary basis transformation matrices by means of Hurwitz matrix equation. Finally,3 to 2 controlled remote preparation protocols of two-qubit states and N to 2 remote preparation protocols of four-qubit cluster states are proposed based on maximally entangled channels and partially entangled channels. Utilizing the maximally entangled channels, the efficiency of these two schemes are both up to 100%. While partial entangled channels, we make use of a specific collective unitary operation and an optimal positive operator-valued measure to restore the desired states in these two protocols and compare these two methods. At present, the research on mulit-source multicast remote state preparation are not sufficient, and is mainly about such protocols in which the information can be only encoded in phase. While in our two protocols, the information can be encoded in the amplitude and phase of desired states.(3) For quantum key distribution protocols, we mainly investigate a kind of quantum key distribution protocols based on channel encryption. Compared with other quantum key distribution protocols, the quantum key distribution protocols based on channel encryption have three outstanding advantages:they needn’t to choose measurement basis, they can be implemented easily and their channel keys are recycled. However, there exists a special entanglement attack in such protocols, by which the attackers can wiretap nearly half of the keys without introducing errors. We focus on the quantum key distribution protocols with Bell states and d-level Bell states as the channel key to find out the essential reasons that they are successfully attacked. Finally, two improved protocols are put forward, although their efficiencies decrease slightly, they are effectively secure against this special entanglement attack.