Detecting Two Kinds Of Quantum Steering In Tripartite Quantum Systems

Quantum nonlocality of quantum mechanics is the core of the problem and have extremely profound physical meaning.The result of the bipartite quantum system is quite rich.On the basis of our predecessors,we will continue to study the quantum steering of the tripartite quantum system.In this paper,the detection problem of AB?C and strong A?BC steering is discussed.Firstly,we give some relationships between the AB?C steering of?ABC and A?C steering of the reduced state ?AC as well as B?C steering of the reduced state ?BC based on their definitions.Secondly,by deducing an inequality(called an steering inequality)for AB?C and strong A?BC unsteerable states,a necessary condition for a quantum state to be AB?C and strong A?BC unsteerable is obtained.Furthermore,the steering radius S(?)of a state p is defined and it is proved that when p is AB?C(or strong A?BC)unsteerable,S(p)?1 and that when S(?)>1,t?+(1-t)? is AB?C(or strong A? BC)steerable for each to<t?1 and for each AB?C(or strong A?BC)unsteerable state ?where t0=2/S(?)+1.Finally,AB?C(or strong A?BC)steerability of the "partial convex combinations" of the GHZ state,generalized GHZ state and the W-state with a AB?C(or strong A?BC)unsteerable state are detected,respectively by using the obtained steering inequality.This paper is divided into three chapters,the specific contents are as follows:The first chapter introduces the related research background and previous research results.The second chapter introduces the scheme of AB?C in the tripartite quantum system,deduces the AB?C steering inequality and proves the concrete example.In the third chapter,we introduce the scheme of A?BC in the tripartite quantum system,derive the strong A?BC steering inequality and prove the concrete examples.