New Constructions And Local Distinguishability Of Orthogonal Product Basis Quantum States

The relationship between entanglement and nonlocality is a fundamental issue in quantum information theory.It has been intensively studied in recent years.One of the most important subjects is to study the local distinguishability of orthogonal quantum states.It is often thought that entanglement leads to the nonlocality of orthogonal quantum states,but this is not always the case.There are orthogonal product states cannot be distinguished by LOCC(Local Operations and Classical Communication),which shows the phenomenon of "nonlocality without entanglement".In addition,if the parties which are far from each other can complete the distinguishable task of the orthogonal product states by LOCC,not only can they complete the information processing task,but also save a lot of resources.Therefore,it is of great practical significance to study how to use less entangled resources to realize the discrimination of the orthogonal product states by LOCC.The above problems are studied in this thesis.We construct new sets of orthogonal product basis states of d (?) d(d?5),and proved its indistinguishability by LOCC.Then we respectively use the maximal and non-maximal entangled state of 2 (?) 2as resources to distinguish the states by LOCC.In chapter 1,we introduce some basic knowledge related to the research content of this thesis,including quantum states,entanglement measure,quantum measurement and distinguishing quantum states.In chapter 2,we use the "image" representation method of quantum state to construct new sets of orthogonal product basis quantum states of d (?) d(d 5)when d is odd and even respectively.We discuss it in two cases when d is odd.Then,we prove the distinguishability of the sets of orthogonal product basis states we constructed by LOCC.In chapter 3,we introduce the image representation method of how to use the maximal entangled resources in the process of distinguishing quantum states briefly.Then we use 2 (?) 2 maximal entangled resources to distinguish the orthogonal product basis states constructed in chapter 2 by LOCC through mathematical induction method.In chapter 4,we generalize the image representation method of using the maximal entangled resources in the process of distinguishing quantum states,such that the nonmaximal entangled resources can also be shown in the image.And we use this method to achieve the partially distinguishable task of the orthogonal product basis states we constructed in chapter 2 by LOCC.