A Bell inequality analog in quantum measure theory

Type of Work

Article

Date

2007

Journal Title

Journal of Physics A: Mathematical and Theoretical

Journal ISSN

1751-8113

Journal Volume

40

First Page

501

Last Page

523

DOI

10.1088/1751-8113/40/3/010

Abstract

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.

Hamilton Areas of Study

Physics

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