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Physical Review Letters

Comment on "Curious Properties of Quantum Ensembles Which Have Been Both Preselected and Post-Selected"

David Z. Albert, Yakir Aharonov, Susan S. D’Amato

Published Jun 2, 1986• 8 citations
Publisher
DOI
10.1103/physrevlett.56.2427

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On Measurable Distinctions between Quantum Ensembles

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A recent result concerning the assignment of well-defined values to certain noncommuting observables in quantum ensembles which have been both preselected and post-selected appears to show that quantum mechanics is "contextual." Extending the argument to the case of measurements on two separated spin-\textonehalf{} systems suggests that quantum mechanics is nonlocal. The significance of these phenomena is evaluated, and it is shown that they have no bearing on the question of contextuality or nonlocality.
We consider quantum ensembles which are determined by pre- and post-selection. Unlike the case of only preselected ensembles, we show that in this case the probabilities for measurement outcomes at intermediate times satisfy causality only rarely; such ensembles can in general be used to signal between causally disconnected regions. We show that under restrictive conditions, there are certain nontrivial bipartite ensembles which do satisfy causality. These ensembles give rise to a violation of the Clauser-Horne-Shimony-Holt inequality, which exceeds the maximal quantum violation given by Tsirelson's bound ${B}_{\mathrm{CHSH}}\ensuremath{\le}2\sqrt{2}$ and obtains the Popescu-Rohrlich bound for the maximal violation, ${B}_{\mathrm{CHSH}}\ensuremath{\le}4$. This may be regarded as an a posteriori realization of supercorrelations, which have recently been termed Popescu-Rohrlich boxes.