A Bell inequality analog in quantum measure theory
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 \sqrt{2} . 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.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- January 2007
- DOI:
- arXiv:
- arXiv:quant-ph/0605008
- Bibcode:
- 2007JPhA...40..501C
- Keywords:
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- Quantum Physics;
- General Relativity and Quantum Cosmology
- E-Print:
- 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