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arXiv:2012.15475

Effects of white noise on Bell theorem for qudits

Arijit Dutta, Jaewan Kim, Jinhyoung Lee

Published Dec 31, 2020• 0 citations
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Abstract

We introduce two types of statistical quasi-separation between local observables to construct two-party Bell-type inequalities for an arbitrary dimensional systems and arbitrary number of measurement settings per site. Note that, the main difference between statistical quasi-separations and the usual statistical separations is that the former are not symmetric under exchange of the two local observables, whereas latter preserve the symmetry. We show that a variety of Bell inequalities can be derived by sequentially applying triangle inequalities which statistical quasi-separations satisfy. A sufficient condition is presented to show quantum violations of the Bell-type inequalities with infinitesimal values of critical visibility $v_c$.

DOI
10.48550/arxiv.2012.15475

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We introduce two types of statistical quasi-separation between local observables to construct two-party Bell-type inequalities for an arbitrary dimensional systems and arbitrary number of measurement settings per site. Note that, the main difference between statistical quasi-separations and the usual statistical separations is that the former are not symmetric under exchange of the two local observables, whereas latter preserve the symmetry. We show that a variety of Bell inequalities can be derived by sequentially applying triangle inequalities which statistical quasi-separations satisfy. A sufficient condition is presented to show quantum violations of the Bell-type inequalities with infinitesimal values of critical visibility vcv_cvc​.
Abstract We introduce two types of statistical quasi-separation between local observables to construct two-party Bell-type inequalities for an arbitrary dimensional systems and arbitrary number of measurement settings per site. Note that, the main difference between statistical quasi-separations and the usual statistical separations is that the former are not symmetric under exchange of the two local observables, whereas latter preserve the symmetry. We show that a variety of Bell inequalities can be derived by sequentially applying triangle inequalities which statistical quasi-separations satisfy. A sufficient condition is presented to show quantum violations of the Bell-type inequalities with infinitesimal values of critical visibility v c.
We specify the local quasi hidden variable (LqHV) model reproducing the probabilistic description of all N-partite joint von Neumann measurements on an N-qudit state. Via this local probability model, we derive a new upper bound on the maximal violation by an N-qudit state of Bell inequalities of any type (either on correlation functions or on joint probabilities) for [Formula: see text] observables per site. This new upper bound not only improves for all [Formula: see text] [Formula: see text] and d the corresponding results available for general Bell inequalities in the literature but also, for the N-qubit case with two observables per site, reduces exactly to the attainable upper bound known for quantum violations of correlation [Formula: see text] setting Bell inequalities in a dichotomic case.
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Bounds, expressed in terms of d and N, on full Bell locality of a quantum state for N≥3N\geq 3N≥3 nonlocally entangled qudits (of a dimension d≥2d\geq 2d≥2) mixed with white noise are known, to our knowledge, only within full separability of this noisy N-qudit state. For the maximal violation of general Bell inequalities by an N-partite quantum state, we specify the analytical upper bound expressed in terms of dilation characteristics of this state, and this allows us to find new general bounds in d,Nd, Nd,N, valid for all d≥2d\geq 2d≥2 and all N≥3N\geq 3N≥3, on full Bell locality under generalized quantum measurements of (i) the N-qudit GHZ state mixed with white noise and (ii) an arbitrary N-qudit state mixed with white noise. The new full Bell locality bounds are beyond the known ranges for full separability of these noisy N-qudit states.
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