Joint Measurability Of POVM Measurement Assemblages And Applications

The POVM measurement assemblage consisting of a set of positive operatorvalue measurements(POVMs)is an important tool for describing and studying the non-locality,quantum steering and quantum correlation of composite quantum systems.In this paper,we first introduce the definition of joint measurability of the POVM measurement assemblage MS consisting of a finite number of POVMs and then prove that the joint measurability of MS is equivalent to its compatibility;We give a general form of a POVM measurement which is jointly measurable with the one-rank projection measurement.It is proved that the POVM measurement assemblage MS is jointly measurable if and only if the corresponding "row stochastic operator matrix" MS composed of MS can be expressed as an "operator convex combination" of {0,IS}-the row stochastic operator matrices.As an application,we obtain some criterions of EPR steering.This paper is divided into three chapters,the specifie contents are as follows:In Chapter 1,we introduce some research backgrounds and status on our main contents,and review some basic definitions of quantum steering and quantum information which will be used in this paper.In Chapter 2,we study the relationship between the joint measurability of MS and its compatibility,and get some important conclusions about joint measurability of POVM measurement assemblages.In Chapter 3,we discuss some criteria of EPR steering,and some examples are given to prove that the maximally entangled state is steering.