A Bell inequality analog in quantum measure theory

@article{Craig2007ABI,
  title={A Bell inequality analog in quantum measure theory},
  author={David Craig and Fay Dowker and Joe Henson and Seth A. Major and David Rideout and Rafael D. Sorkin},
  journal={Journal of Physics A},
  year={2007},
  volume={40},
  pages={501-523}
}
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… 
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31 Citations
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References

SHOWING 1-10 OF 48 REFERENCES
Quantum Measure Theory and its Interpretation
We propose a realistic, spacetime interpretation of quantum theory in which reality constitutes a *single* history obeying a "law of motion" that makes definite, but incomplete, predictions about its…
Logical reformulation of quantum mechanics. I. Foundations
The basic rules of quantum mechanics are reformulated. They deal primarily with individual systems and do not assume that every ket may represent a physical state. The customary kinematic and dynamic…
Quantum mechanics as quantum measure theory
The additivity of classical probabilities is only the first in a hierarchy of possible sum rules, each of which implies its successor. The first and most restrictive sum rule of the hierarchy yields…
Stochastic Einstein-locality and the Bell theorems
Standard proofs of generalized Bell theorems, aiming to restrict stochastic, local hidden-variable theories for quantum correlation phenomena, employ as a locality condition the requirement of…
Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime
These are the author's lectures at the 1992 Les Houches Summer School, "Gravitation and Quantizations". They develop a generalized sum-over-histories quantum mechanics for quantum cosmology that does…
Some Identities for the Quantum Measure and its Generalizations
TLDR
A generalized measure theory based on a hierarchy of ``sum-rules'' yields classical probability theory, and the first sum-rule yields a generalized probability theory that includes quantum mechanics as a special case.
Quantum Mechanics in the Light of Quantum Cosmology
We sketch a quantum mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the quasiclassical domain…
Nonlocal correlations as an information-theoretic resource
It is well known that measurements performed on spatially separated entangled quantum systems can give rise to correlations that are nonlocal, in the sense that a Bell inequality is violated. They…
The Classification of decoherence functionals: An Analog of Gleason's theorem
Gell‐Mann and Hartle have proposed a significant generalization of quantum theory with a scheme whose basic ingredients are ‘‘histories’’ and decoherence functionals. Within this scheme it is natural…
Quantum analogues of the Bell inequalities. The case of two spatially separated domains
One Investigates inequalities for the probabilities and mathematical expectations which follow from the postulates of the local quantum theory. It turns out that the relation between the quantum and…
...
...