A Bell inequality analog in quantum measure theory

  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},
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… 
The regular histories formulation of quantum theory
It can be argued that RH compares favourably with other proposed interpretations of quantum mechanics in that it resolves the measurement problem while retaining an essentially classical worldview without parallel universes, a framework-dependent reality or action-at-a-distance.
How to Measure the Quantum Measure
The histories-based framework of Quantum Measure Theory assigns a generalized probability or measureμ(E) to every (suitably regular) set E of histories. Even though μ(E) cannot in general be
Three-Slit Experiments and Quantum Nonlocality
An interesting link between two very different physical aspects of quantum mechanics is revealed; these are the absence of third-order interference and Tsirelson’s bound for the nonlocal
Quantum Measure Theory: A New Interpretation
Quantum measure theory can be introduced as a histories based reformulation (and generalisation) of Copenhagen quantum mechanics in the image of classical stochastic theories. These classical models
Popescu-Rohrlich boxes in quantum measure theory
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 set-up under the assumption that
Quantum dynamics without the wavefunction
When suitably generalized and interpreted, the path integral offers an alternative to the more familiar quantal formalism based on state vectors, self-adjoint operators and external observers.
Thermodynamics and the structure of quantum theory
This work studies how compatibility with thermodynamics constrains the structure of quantum theory by studying how self-duality and analogues of projective measurements, subspaces and eigenvalues imply important aspects ofquantum theory.
Bounding Quantum Contextuality with Lack of Third-Order Interference.
  • J. Henson
  • Philosophy
    Physical review letters
  • 2015
It is shown that the lack of irreducible third-order interference implies the principle known as the E principle or consistent exclusivity (that, if each pair of a set of experimental outcomes are exclusive alternatives in some measurement, then their probabilities are consistent with the existence of a further measurement in which they are all exclusive).
Logic is to the quantum as geometry is to gravity
I will propose that the reality to which the quantum formalism implicitly refers is a kind of generalized history, the word history having here the same meaning as in the phrase sum-over-histories.
On Noncontextual, Non-Kolmogorovian Hidden Variable Theories
One implication of Bell’s theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability


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
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