Theoretical Study Of Quantum State Discrimination And Quantum Correlations

Assume that a state of a quantum system is one of N states, and how to identify thegiven state in quantum mechanics is called quantum state discrimination. Quantum statediscrimination is useful in many tasks in quantum information processing and quantumcomputation. Therefore, it was widely discussed recently. Meanwhile, quantum entan-glement plays an significant role in quantum computation and quantum information, andit is possible to achieve some tasks with entanglement which are impossible in classicalcomputation and classical information theory. Recently, it is showed that quantum cor-relation is more general than quantum entanglement as a kind of quantum non-locality,and it can be explained as the reasons for the speedup of some quantum algorithms overclassical ones. So, quantum correlation has also attracted much attention currently. Thisdissertation devotes to these two fundamental issues, and the author presents the resultsobtained in his study toward a Ph.D Degree in detail. To be more specific,First, the author studies the discrimination between two photon polarizations inmoving frames. The transformations of photon polarization in moving frames are con-sidered, which are relative to photon’s momentum. In both unambiguous discriminationand minimum-error discrimination, the results of state discriminations are dependent onthe relative velocity of detectors, and the influence is significant when the velocity islarge enough.Secondly, theauthorgeneralizestheprogrammablediscriminationbetweentwoun-known states to the high-dimensional case, and obtains the optimal successful probabil-ity and POVM operators in the optimal unambiguous discrimination. Furthermore, ascheme is proposed to realize the programmable discrimination in the optical experi-ment. Then, the author considers a more general case, the multi-copy programmablediscrimination between two high-dimensional unknown states. With the representationtheory of U(n) group, the analytical results and measurement operators for both the op-timal unambiguous discrimination and minimum-error discrimination are derived.Thirdly, the author considers the density matrix form in the coherence-vector rep-resentation. The description of the orthogonal measurement is also given in coherence-vector representation, which is a projector operator. Meanwhile, a criterion tensor isdefined, which can be used to verify the correlation of a bipartite state. A different measure of correlations is also proposed, and analytical expressions for this measure areavailable for any bipartite states.