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 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 Bell's perfect correlations or anticorrelations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-25,
author = {Elena R. Loubenets},
title = {Quantum states satisfying classical probability constraints},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {325-337},
zbl = {1134.81317},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-25}
}
Elena R. Loubenets. Quantum states satisfying classical probability constraints. Banach Center Publications, Tome 72 (2006) pp. 325-337. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-25/