Popescu-Rohrlich Boxes in Quantum Measure Theory
arXiv:quant-ph/0605253 · doi:10.1088/1751-8113/40/26/011
Abstract
Two results are proved at the quantal level in Sorkin's hierarchy of measure theories. One is a strengthening of an existing bound on the correlations in the EPR-Bohm setup under the assumption that the probabilities admit a strongly positive joint quantal measure. It is also proved that any set of no-signalling probabilities, for two distant experimenters with a choice of two alternative experiments each and two possible outcomes per experiment, admits a joint quantal measure, though one that is not necessarily strongly positive.
10 pages, 1 figure, LaTeX, acknowledgement added; Dedicated to Rafael Sorkin on the occasion of his 60th birthday
References in corpus (9)
- Non-local correlations as an information theoretic resource
- Quantum Mechanics as Quantum Measure Theory
- Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School)
- Quantum Measure Theory and its Interpretation
- Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime
- The Random Walk in Generalized Quantum Theory
- Some Identities for the Quantum Measure and its Generalizations
- Generalizing Quantum Mechanics for Quantum Spacetime
- A Bell Inequality Analog in Quantum Measure Theory
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