On Some Problems About Quatum Information Processing

In recent years,quantum information processing has been developing rapidly and achieve much attention because of its huge potential of applications.Quantum entan-glement and quantum nonlocality,as the foundation of quantum information theory,are crucial for quantum computation and quantum secret communication tasks and is hot in the study of quantum information processing.To study the intrinsic relation between quantum entanglement and quantum nonlocality,we can not only complete and enrich the theory of quantum information,but also exploit their power in real application of quan-tum information processing task more efectively.Moreover,mutually unbiased bases are also useful in many quantum information processing scene,but for the mutually unbiased bases in multipartite systems,little is known to us about their relation between quantum entanglement.In this paper,we mainly study the problem of distinguishing orthogonal quantum states and constructing mutually unbiased entangled bases.For the problem of distin-guishing orthogonal quantum states,we consider in Chapter ? and Chapter IV respec-tively two different types of maximally entangled states(MESs):the lattice MESs and the generalized Bell states.In Chapter V,we study the construction of mutually unbiased unextendible maximally entangled bases(MUUMEBs).More explicitly,we present our results as follows:?.For the problem of locally distinguishing lattices MESs,we study their PPT distin-guishability by using the method of semidefinite pragram.When t=2,namely on C4(?)C4,we are able to construct all sets of 4 orthogonal PPT indistinguishable lattice MESs and find some interesting properties about them.For the case t=3 and t=4,we prove that all of the small sets of orthogonal lattice MESs are PPT distinguishable.We conjecture that when t is larger,the results are similar:all small sets of lattice MESs are PPT distinguishable.?.For generalized Bell states,we study the problem of distinguishing them with only one direction of communication only.By the equivalence of the one-way distin-guishability of a set of generalized Bell state to the existence of solution about cer-tain set of equations,we successfully construct a small set of Bell states in Cd(?)Cd that is indistinguishable with one-way LOCC.?.For the construction of mutually unbiased unextendible maximally entangled bases,by using some results from the theory of finite fields,we extend the presently known result on C2(?)C3 to more system of higher dimension such as C4(?)C5,C6(?)C7,C10(?)C11,etc.We also point out that this method is suitable for certain specific systems.