2006/05/31 by David Craig, Fay Dowker, Joe Henson +4
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #gr-qc #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/3/010
published as J.Phys.A40:501-523,2007 · 38 pages, TeX. Several changes and added comments to bring out the meaning more clearly. Minor rewording and extra acknowledgements, now closer to published version
arxiv created 2006/12/11 · openalex publication_date 2006/12/20 · arxiv updated 2010/04/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
One obtains Bell's inequalities if one posits a hypothetical joint probability distribution, or measure , whose marginals yield the probabilities produced by the spin measurements in question. The existence of a joint measure is in turn equivalent to a certain causality condition known as 'screening off'. We show that if one assumes, more generally, a joint quantal measure , or 'decoherence functional', one obtains instead an analogous inequality weaker by a factor of . The proof of this 'Tsirel'son inequality' is geometrical and rests on the possibility of associating a Hilbert space to any strongly positive quantal measure. These results lead both to a question : 'Does a joint measure follow from some quantal analog of 'screening off'?', and to the observation that non-contextual hidden variables are viable in histories-based quantum mechanics, even if they are excluded classically.