An Unentangled Gleason's Theorem

2000/02/22 by Nolan R. Wallach, Wallach, Nolan R. · 2 citations
Mathematics · Physics and Astronomy · Psychology · #History and Theory of Mathematics #Philosophy and Theoretical Science #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0002058

9 pages, no figures

arxiv created 2000/02/22 · arxiv updated 2009/12/01

Abstract

The purpose of this note is to give a generalization of Gleason's theorem inspired by recent work in quantum information theory on "nonlocality without entanglement." For multipartite quantum systems, each of dimension three or greater, the only nonnegative frame functions over the set of unentangled states are those given by the standard Born probability rule. However, if one system is of dimension 2 this is not necessarily the case.

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