三体量子系统中AB→C导引的探测

Detecting AB→C steering in tripartite quantum systems

本文基于三体量子系统中量子导引方案的概念与已有的等价刻画,研究AB→C导引的探测问题.首先,揭示了三体量子态ρABC的AB→C可导引性与其约化态ρAC的A→C可导引性及约化态ρBC的B→C可导引性之间的关系;其次,通过推导出AB→C不可导引态必须满足的一个不等式(称为导引不等式),得到了量子态为AB→C不可引导态的必要条件.基于导引不等式,我们引入了量子态ρ的导引半径S (ρ),并且证明,当ρ是AB→C不可导引态时, S (ρ)≤1;当S (ρ)> 1时,ρ与任意AB→C不可导引态η的凸组合tρ+(1-t)η都是AB→C可导引的,其中t0:=2/S (ρ)+1<t≤1.最后,作为导引不等式的应用,证明了三体GHZ态、广义GHZ态及W-态与任意AB→C不可导引态的"部分凸组合"的AB→C可导引性.

In this paper,the detection problem of AB→C steering is discussed.Firstly,we give some relationships between the AB→C steering ofρABC and A→C steering of the reduced stateρAC as well as B→C steering of the reduced stateρBC based on their definitions.Secondly,by deducing an inequality(called an steering inequality)for AB→C unsteerable states,a necessary condition for a quantum state to be AB→C unsteerable is obtained.Furthermore,the steering radius S(ρ)of a stateρis defined and it is proved that whenρis AB→C unsteerable,S(ρ)≤1 and that when S(ρ)>1,tρ+(1-t)ηis AB→C steerable for each t0<t≤1 and for each AB→C unsteerable stateηwhere t0=2/S(ρ)+1.Finally,AB→C steerability of the"partial convex combinations"of the GHZ state,generalized GHZ state and the W-state with a AB→C unsteerable state are detected,respectively by using the obtained steering inequality.