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Indistinguishability and Negative Probabilities.

J Acacio de Barros1, Federico Holik2

  • 1School of Humanities and Liberal Studies, San Francisco State University, San Francisco, CA 94132, USA.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

Quantum systems

Keywords:
contextualityindistinguishabilitynegative probabilitiesquantum ontologyquasi-set theorysigned measure

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Area of Science:

  • Quantum mechanics
  • Foundations of physics

Background:

  • Quantum systems exhibit unique properties like indistinguishability.
  • The interpretation of quantum probabilities is an ongoing area of research.
  • Signed probabilities and quantum contextuality are advanced concepts.

Purpose of the Study:

  • To investigate the link between quantum indistinguishability and signed probabilities.
  • To develop a measure-theoretic framework for signed probabilities.
  • To explore the implications of ontological indistinguishability in quantum mechanics.

Main Methods:

  • Introduced a measure-theoretic definition of signed probabilities.
  • Drew inspiration from research in quantum contextuality.
  • Formulated arguments connecting indistinguishability to core quantum principles.

Main Results:

  • Demonstrated that indistinguishability implies the no-signaling condition.
  • Showed that ontological indistinguishability leads to negative probabilities.
  • Established a formal connection between fundamental quantum properties and probability theory.

Conclusions:

  • Quantum indistinguishability is fundamentally linked to the emergence of signed probabilities.
  • The no-signaling condition arises naturally from indistinguishable quantum systems.
  • This work provides new insights into the foundational aspects of quantum probability.