David Craig et al 2007 J. Phys. A: Math. Theor. 40 501 doi:10.1088/1751-8113/40/3/010
A Bell inequality analog in quantum measure theory
David Craig1,2, Fay Dowker3,4, Joe Henson5, Seth Major6, David Rideout3 and Rafael D Sorkin4,7
Show affiliationsOne 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.
- PACS
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03.65.Yz Decoherence; open systems; quantum statistical methods
03.65.Ta Foundations of quantum mechanics; measurement theory
- MSC
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81S25 Quantum stochastic calculus
81P15 Quantum measurement theory
81S10 Geometry and quantization, symplectic methods (See also 53D50)
- Subjects
- Dates
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Issue 3 (19 January 2007)
Received 4 August 2006, in final form 15 November 2006
Published 20 December 2006
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A Bell inequality analog in quantum measure theory
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