Research On Quantum Cryptography And Measure Of Entanglement

The combination between quantum information physics and information sci-ence leads to the emergency of a new interdiscipline - the birth of quantum information. The research field of quantum information and quantum com-putation(QIQC), an interdisciplinary field which involves quantum mechanics, computer science and the theory of information, has attacted more and more interests. Quantum entanglement attracts much attention from many researchers due to the fact that it plays an important role in QIQC as a valuable resouce. Investigation concerning quantum entanglement is wide from its basic definitions to applications to experiment. We develop the research from two side on the basis of quantum entanglement.One is how to realize an secure and high efficient quantum key distribution by using different kind entangled states. Based on controlled order rearrange encryption (CORE) for quantum key distribution using EPR pairs, we propose the generalized controlled order rearrangement encryption (GCORE) protocols of N qubits and N qutrits, concretely display them in the cases using 3-qubit, 2-qutrit maximally entangled basis states. We further indicate that our protocols will become safer with the increase of number of particles and dimensions. Moreover, we carry out the security analysis using quantum covariant cloning machine for the protocol using qutrits. Although the applications of the generalized scheme need to be further studied, the GCORE has many distinct features such as great capacity and high efficiency. Besides, we propose a generalized controlled order rearrangement encryption (GCORE) protocols using non-maximally entangled W-class states with probability, but it also has full efficiency and we compare the similarity and difference with original protocol. Finally, we use this W-class state to split quantum information, thus the scheme is robust against decoher-ence.Another is the research which is quantificational measurement and qualitative classification. We revise the geometric measure of entanglement (GME). The revised geometric measure of entanglement (RGME) is an entanglement monotone. Some useful inequalities about RGME are deduced. As the RGME's application, the two-parameter class of states in 2 (?) n quantum system, the two particles high dimensional maximally entangled mixed state, the isotropic state including n-particle d-level case and two multipartite bound entangled states are calculated. The result shows there is a relation calculated. The result shows there is a relation , which indicates thatthe RGME is an appropriate measure of entanglement.In this paper the entanglement of pure 4-qubit states is discussed. We classify 4-qubit pure states under the stochastic local operation and classical communication (SLOCC). There exist twenty three essentially different classes of states, giving rise to a four-graded partially ordered structure. We also give the methods to judge which class an arbitrary 4-qubit state belongs to. Finally, we re-classify 4-qubit state from 2×2×2, 4×4 aspects. Besides, we discuss the classification difference of several methods for 3-qubit pure state.The thesis is organized as follows: In Chap.1 we provide generalized controlled order rearrange encryption (GCORE) protocol, GCORE using W-class state with probability and secret splitting scheme using W-class state. In Chap 2, the revised geometric measure of entanglement (RGME) is presented, applying it into the discrete and continuous variable systems. In Chap 3. we make some discussion about the 4-qubit pure state. In Chap.4 a brief summary is given.