In general, for a bipartite quantum system
Cd⊗Cd and an integer
k such that
4≤k≤d,there are few necessary and sufficient conditions for local discrimination of sets of
k generalized Bell states (GBSs) and it is difficult to locally distinguish
k-GBS this http URL this paper, we consider the local discrimination of GBS sets and the purpose is to completely solve the problem of local discrimination of GBS sets in some bipartite quantum systems,specifically, we show some necessary and sufficient conditions for local discrimination of GBS sets by which the local discrimination of GBS sets can be quickly determined.Firstly some sufficient conditions are given, these sufficient conditions are practical and effective.Fan
,s and Wang et al.
,s results (Phys Rev Lett 92:177905, 2004: Phys Rev A 99:022307, 2019) can be deduced as special cases of these conditions.Secondly in
C4⊗C4, a necessary and sufficient condition for local discrimination of GBS sets is provided,all locally indistinguishable 4-GBS sets are found,and then we can quickly determine the local discriminability of an arbitrary GBS this http URL
C5⊗C5, a concise necessary and sufficient condition for one-way local discrimination of GBS sets is obtained,which gives an affirmative answer to the case
d=5 of the problem proposed by Wang et al. (Phys Rev A 99:022307, 2019).
Abstract We present a single general Bell inequality that summarizes all possible Bell type constrains on the correlation function for the N‐particle system (i.e., it is a necessary and sufficient condition for the existence of local realistic models for the correlation function). It is applicable in the case when measurements on each particle can be chosen between two arbitrary dichotomic observables. We also obtain a necessary and sufficient condition for an arbitrary N‐qubit mixed state to violate this general Bell inequality.
It has been believed that statistical inequalities such as the Bell inequality should be modified once measurement independence (MI), the assumption that observers can freely choose measurement settings without changing the probability distribution of hidden variables, is relaxed. However, we show that there exists the possibility that the Bell inequality is still valid even if MI is relaxed. MI is only a sufficient condition to derive the Bell inequality when both determinism and setting independence, usually called local realism, are satisfied. We thus propose a condition necessary and sufficient for deriving the Bell inequality, called concealed measurement dependence.