Threshold bounds for noisy bipartite states

Abstract

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".

9 pages; v.2: minor editing corrections; to appear in J. Phys. A: Math. Gen

References in corpus (2)

• Class of bipartite quantum states satisfying the original Bell inequality
• On separability of quantum states and the violation of Bell-type inequalities

Cited by in corpus (6)

• Local quasi hidden variable modelling and violations of Bell-type inequalities by a multipartite quantum state
• On the probabilistic description of a multipartite correlation scenario with arbitrary numbers of settings and outcomes per site
• Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations
• Context-invariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space
• Local hidden variable modelling, classicality, quantum separability, and the original Bell inequality
• Full Bell locality of a noisy state for $N\ge 3$ nonlocally entangled qudits