63 research outputs found
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
Quantifying tolerance of a nonlocal multi-qudit state to any local noise
We present a general approach for quantifying tolerance of a nonlocal
N-partite state to any local noise under different classes of quantum
correlation scenarios with arbitrary numbers of settings and outcomes at each
site. This allows us to derive new precise bounds in d and N on noise
tolerances for: (i) an arbitrary nonlocal N-qudit state; (ii) the N-qudit
Greenberger-Horne-Zeilinger (GHZ) state; (iii) the N-qubit W state and the
N-qubit Dicke states, and to analyse asymptotics of these precise bounds for
large N and d.Comment: 16 page
Quantum states satisfying classical probability constraints
For linear combinations of quantum product averages in an arbitrary bipartite
state, we derive new quantum Bell-form and CHSH-form inequalities with the
right-hand sides expressed in terms of a bipartite state. This allows us to
specify in a general setting bipartite state properties sufficient for the
validity of a classical CHSH-form inequality and the perfect correlation form
of the original Bell inequality for any bounded quantum observables. We also
introduce a new general condition on a bipartite state and quantum observables
sufficient for the validity of the original Bell inequality, in its perfect
correlation or anticorrelation forms. Under this general sufficient condition,
a bipartite quantum state does not necessarily exhibit perfect correlations or
anticorrelations.Comment: v.2: 13 pages, reorganized and shortened version (most examples
removed); one reference added; the results not change
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