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Contextuality in Phase Space.

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We developed a new framework for testing quantum contextuality in phase space. This approach unifies continuous and discrete systems for easier experimental tests of quantum mechanics.

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Area of Science:

  • Quantum mechanics
  • Quantum information theory
  • Quantum foundations

Background:

  • Contextuality is a key feature of quantum mechanics, challenging classical intuition.
  • Existing contextuality tests often rely on specific experimental setups.
  • Phase space representations offer an alternative perspective on quantum phenomena.

Purpose of the Study:

  • To present a general framework for contextuality tests in phase space.
  • To derive a condition for displacement operators in contextuality scenarios.
  • To unify contextuality tests across continuous and discrete quantum systems.

Main Methods:

  • Utilizing displacement operators in phase space.
  • Deriving a general condition for single-mode displacement operators.
  • Applying the framework to Peres-Mermin square and similar scenarios.
  • Extending the approach to finite-dimensional systems using Heisenberg-Weyl operators.

Main Results:

  • A general condition for displacement operators enabling contextuality tests was derived.
  • The framework provides a unified approach for both continuous and discrete phase space systems.
  • The method simplifies experimental implementation through modular variable measurements.

Conclusions:

  • The proposed framework offers a unified and geometrically intuitive view of quantum contextuality.
  • This approach facilitates experimental verification of quantum contextuality across different systems.
  • The findings contribute to a deeper understanding of the foundations of quantum mechanics.