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arXiv:quant-ph/0405058

Error in an argument regarding "improper" mixtures

Kirkpatrick, K. A.

Published May 11, 2004• 0 citations
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Abstract

An argument, perhaps originating with Feyerabend a half century ago, and repeated many times since, purporting to establish that an "ignorance interpretation" of a bipartite pure entangled state leads to logical inconsistency, is incorrect: the argument fails to account for the effects of indistinguishability.
DOI
10.48550/arxiv.quant-ph/0405058

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All quantum mixtures are what d'Espagnat has termed "improper." His "proper" mixture cannot be created -- if welcher weg, or distinguishing, information exists, an improper mixture results, while in the absence of such information, the resulting "mixture" is a pure state. D'Espagnat has claimed that an interpretation of the improper mixture in terms of subensembles leads to logical inconsistency; this claim is shown to be incorrect, as d'Espagnat's argument fails to account for the indistinguishability of the pure-state subensembles.
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Experimental evidence, the heuristics of indistinguishability, and its logical inconsistency with quantum formalism all argue against the existence of a quantum mixture uncorrelated with the exterior, that is, argue for the postulate "The state of a system uncorrelated with its exterior is pure." This is shown to be equivalent with "The state of a system describable in terms of indistinguishable pure states is pure," and with "The state of the universe is pure"; further, it yields a quantitative expression of the traditional relation of welcher Weg information to partial coherence. It is concluded that all mixtures are "improper," the trace-reduction of a composite system's pure state.