Partial Steerability And Nonlocality Of Multipartite Quantum States

Quantum nonlocality means usually the correlations between subsystems of a composite quantum system,including Bell nonlocality,steerability,quantum entanglement,and quantum discord.It is well-known that these types of quantum nonlocality are important resources in quantum Quantum communication,quantum computing,as well s quantum information processing and therefore become hot fields in the of quantum information.In this thesis,we propose and discuss partial steerability and nonlocality of multipartite quantum states,leading to some new methods for detecting steerability and Bell nonlocal of multipartite states.In Chapter 1,we introduce some basic concepts,such as quantum systems,state spaces,quantum states,density operators,partial traces,POVM measurements and so on.In Chapter 2,using a POVM measurement assemblage on the ith subsystem,we give the definitions of the unsteerability and steerability from i to j for multipartite quantum states,called partial unsteerability and partial steerability;obtain a sufficient condition that a quantum state p is steerable from i to j by establishing necessary conditions for quantum state to be unsteerable from i to j.In Chapter 3,using POVM measurement assemblages on the ith and jth subsystems,we introduce the concepts of(i,j)-Bell locality and(i,j)-Bell nonlocality for multipartite quantum states,called(i,j)-Bell locality and partial(i,j)-Bell nonlocality;derive a sufficient condition for a quantum state p to be(i,j)-Bell nonlocal by establishing some necessary conditions for a quantum state to be(i,j)-Bell local.In Chapter 4,we give a summary of the research results obtained in this thesis and propose some questions to be discussed in the future research.