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Classical (Local and Contextual) Probability Model for Bohm-Bell Type Experiments: No-Signaling as Independence of

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  • 1Mechanics and Optics (ITMO) Department, National Research University for Information Technology, St. Petersburg 197101, Russia.

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Summary
This summary is machine-generated.

Quantum probabilities in Bohm-Bell type experiments can be represented as classical conditional probabilities. This framework applies to diverse fields beyond physics, including social sciences and economics.

Keywords:
(no-)signalingBohm–Bell type experiments in physics and psychologycontextual hidden-variables modelslocaltyquantum versus classical probabilityrandom generatorsselection of experimental settings, conditional probability

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Area of Science:

  • Quantum mechanics
  • Foundations of physics
  • Probability theory

Background:

  • Classical probability representations of quantum states and observables are foundational.
  • Bohm-Bell type experiments probe the nature of quantum correlations.

Purpose of the Study:

  • To express quantum correlations in Bohm-Bell type experiments using classical random variables.
  • To develop a conditional probability model for local contextual hidden-variables.
  • To characterize signaling phenomena within this framework.

Main Methods:

  • Review of classical probability representations.
  • Development of a conditional probability model based on experimental settings.
  • Application of the model to characterize signaling.

Main Results:

  • Correlations in Bohm-Bell type experiments are shown to be expressible as correlations of classical random variables.
  • A local contextual hidden-variables model is formulated using conditional probabilities.
  • The conditional probability approach is used to characterize (no-)signaling.

Conclusions:

  • Quantum probabilities and probabilities in Bohm-Bell type experiments can be classically represented as conditional probabilities.
  • This classical representation extends beyond physics to fields like psychology, sociology, and economics.
  • The framework provides a unified approach to understanding probabilities in diverse experimental and theoretical contexts.