Threshold bounds for noisy bipartite states

For a nonseparable bipartite quantum state violating the Clauser-Horne-Shimony-Holt (CHSH) inequality, we evaluate amounts of noise breaking the quantum character of its statistical correlations under any generalized quantum measurements of Alice and Bob. Expressed in terms of the reduced states, these new threshold bounds can be easily calculated for any concrete bipartite state. A noisy bipartite state, satisfying the extended CHSH inequality and the perfect correlation form of the original Bell inequality for any quantum observables, neither necessarily admits a local hidden variable model nor exhibits the perfect correlation of outcomes whenever the same quantum observable is measured on both "sides".Comment: 9 pages; v.2: minor editing corrections; to appear in J. Phys. A: Math. Ge

Class of bipartite quantum states satisfying the original Bell inequality

In a general setting, we introduce a new bipartite state property sufficient for the validity of the perfect correlation form of the original Bell inequality for any three bounded quantum observables. A bipartite quantum state with this property does not necessarily exhibit perfect correlations. The class of bipartite states specified by this property includes both separable and nonseparable states. We prove analytically that, for any dimension d>2, every Werner state, separable or nonseparable, belongs to this class.Comment: 6 pages, v.2: one reference added, the statement on Werner states essentially extended; v.3: details of proofs inserte

On the probabilistic description of a multipartite correlation scenario with arbitrary numbers of settings and outcomes per site

We consistently formalize the probabilistic description of multipartite joint measurements performed on systems of any nature. This allows us: (1) to specify in probabilistic terms the difference between nonsignaling, the Einstein- Podolsky-Rosen (EPR) locality and Bell's locality; (2) to introduce the notion of an LHV model for an S_{1}x...xS_{N}-setting N-partite correlation experiment, with outcomes of any spectral type, discrete or continuous, and to prove both general and specific "quantum" statements on an LHV simulation in an arbitrary multipartite case; (3) to classify LHV models for a multipartite quantum state, in particular, to show that any N-partite quantum state, pure or mixed, admits an Sx1x...x1 -setting LHV description; (4) to evaluate a threshold visibility for a noisy bipartite quantum state to admit an S_{1}xS_ {2}-setting LHV description under any generalized quantum measurements of two parties. In a sequel to this paper, we shall introduce a single general representation incorporating in a unique manner all Bell-type inequalities for either joint probabilities or correlation functions that have been introduced or will be introduced in the literature.Comment: 26 pages; added section Conclusions and some references for section

General Framework for the Behaviour of Continuously Observed Open Quantum Systems

We develop the general quantum stochastic approach to the description of quantum measurements continuous in time. The framework, that we introduce, encompasses the various particular models for continuous-time measurements condsidered previously in the physical and the mathematical literature.Comment: 30 pages, no figure

Reexamination of a multisetting Bell inequality for qudits

The class of d-setting, d-outcome Bell inequalities proposed by Ji and collaborators [Phys. Rev. A 78, 052103] are reexamined. For every positive integer d > 2, we show that the corresponding non-trivial Bell inequality for probabilities provides the maximum classical winning probability of the Clauser-Horne-Shimony-Holt-like game with d inputs and d outputs. We also demonstrate that the general classical upper bounds given by Ji et al. are underestimated, which invalidates many of the corresponding correlation inequalities presented thereof. We remedy this problem, partially, by providing the actual classical upper bound for d less than or equal to 13 (including non-prime values of d). We further determine that for prime value d in this range, most of these probability and correlation inequalities are tight, i.e., facet-inducing for the respective classical correlation polytope. Stronger lower and upper bounds on the quantum violation of these inequalities are obtained. In particular, we prove that once the probability inequalities are given, their correlation counterparts given by Ji and co-workers are no longer relevant in terms of detecting the entanglement of a quantum state.Comment: v3: Published version (minor rewordings, typos corrected, upper bounds in Table III improved/corrected); v2: 7 pages, 1 figure, 4 tables (substantially revised with new results on the tightness of the correlation inequalities included); v1: 7.5 pages, 1 figure, 4 tables (Comments are welcome