Study On Quantum Information Theory Based On Quantum Correlation

Quantum information is a new interdisciplinary science, which is based on quantum mechanics theory to encode, transmit, and process information. It can overcome limitations and disadvantages of classical computer science and communication theory,such as its superiority in solving prime factorization of large numbers, discrete logarithm problem, and quantum communication is much more securer than classical one.On the background of correlation in quantum theory, this thesis is devoted to study several typical quantum communication proposals and operator convex function theory and its application in quantum information theory. The main work is as following:1. By using the asymmetric W state with entanglement correlation as part of a shared quantum channel, quantum teleportation and superdense coding protocols are completed.We first design three quantum teleportation schemes, including teleportation of a single qubit, two-qubit and an arbitrary N-qubit. All the teleportation processes can be achieved with unit probability. Then we study the superdense coding of five and(2N + 1) classical bits between two parties. In all the superdense coding protocols, the senders only need to apply simple operations like I, X and Z, and the successful probability is one.2. Based on the idea of remote state preparation, the controlled remote state preparation of a single qubit and a two-qubit via generalized Schmidt decomposition of a general three-qubit pure state is researched. The general three-qubit pure state is not equivalent to GHZ and W states in the sense of local operation and classical communication, thus the entanglement property is different from them essentially.3. By employing the maximally entangled GHZ states, the joint remote state preparation between multi-parties is studied. Firstly, we study the joint remote state preparation between N senders and two receivers. Secondly, the joint remote state preparation with N senders and three receivers is researched. In the joint remote state preparation between multi-parties, the classical information is distributed jointly in form of amplitude set and phase set. The proposed schemes are applicable to real cases as well as complex cases.The receivers only need to apply simple Pauli operations to recover the prepared state,which is conducive to receivers in poor experimental environment. In the last, we give the security analysis of the proposals, which shows that the proposed schemes are security against conspiracy inside attacks as well as entangled attacks.4. On the base of typical operator convex functions and perspectives of regular operator mappings, operator convex function of several variables and its application in quantum information theory is investigated. Firstly, some two variable functions are proved to be operator convex(or concave). Based on it, the Fr′echet differential of power function f(t) = tp+1, 0 < p < 1 is shown to be operator concave. Secondly, by using the perspectives of regular operator mappings of several variables, some functions of three variables are shown to be operator convex(or concave), and the concavity theorem of Lieb is obtained as a spacial case of our examples. As there are few known operator convex functions of several variables, the obtained new functions could be used in quantum information theory.5. The characterization of capacity of quantum channel via Wigner-Yanase skew information is studied. We first conclude two methods of calculating global information content. The difference of global information content before and after quantum operation is considered as a characterization of capacity of quantum channel. By investigating into typical quantum channels, we discover that the characterization via global information content is consistent with decorrelation measurement of quantum channel.