Research On The Nonlocality Of Orthogonal Quantum States

The local distinguishability of orthogonal quantum states is the basic theory of quantum computation and quantum information.It has importmant application in distributed quantum computation and quantum cryptography,and is a research hotspot in the field of quantum information processing.The local discrimination of orthogonal quantum states means that a quantum state is randomly selected from a set of known orthogonal quantum states,and the information of this state is determined only by local operations and classical communication,which doesn't require quantum communication and global operations.If one set of orthogonal quantum states cannot be locally distinguished,it means that the set of quantum states is nonlocal.Therefore,on the one hand,the study of this problem will help to better save communications and operational resources in practical application.On the other hand,it is also a very effective means to explore the relationship between quantum entanglement and quantum nonlocality,and benefit to better understand the theory of quantum nonlocality.This dissertation mainly studies the local distinguishability of two classes of very special orthogonal quantum states,namely product states and maximally entangled states.The details are as follows.1.In the construction of nonlocality of orthogonal product states,this dissertation first present a method to construct orthogonal product bases which cannot be locally distinguished in d(?)d quantum system,in which d is odd.This result once again demonstrates the peculiar phenomenon of "nonlocality without entanglement".Then,for d(?)d quantum system,a class of different orthogonal product bases is constructed and proved to be locally indistinguishable.Furthermore,this result is extended to the general bipartite quantum systems.Finally,using some locally indistinguishable orthogonal product states in bipartite quantum systems,we present three general methods to construct the nonlocality of orthogonal product states in multipartite quantum systems.2.In the research of local distinguishability of maximally entangled states,this dissertation first presents a necessary and sufficient condition for one-way locally distinguishing the generalized Bell states.Using this result,we construct three sets of one-way locally indistinguishable maximally entangled states.Then,in d(?)d quantum system,based on the Fourier transform of the additive group,we construct a very small number of maximally entangled states and prove that these states cannot be one-way locally distinguished.Finally,this dissertation gives a simple and effective method to judge the one-way local distinguishability of the generalized Bell states.3.In entanglement-assisted discrimination of orthogonal quantum states,for a class of locally indistinguishable orthogonal product states,we prove these states can be locally distinguished with the help of one copy of 2(?)2 maximally entangled states.Then,considering two different kinds of orthogonal product states,we present one protocol to locally distinguish these states with the help of multiple copies of 2(?)2 maximally entangled states.When the dimensions and types of locally distinguished quantum states change,the single copy of high-dimensional entanglement resources used in previous protocols also need to change.But our method requires only one device which can prepare the same kind of low-dimensional entanglement resources,and only changes in the number of preparation.It is beneficial to be applied in experiment and save entanglement resources.