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All Incompatible Sets of Measurements Can Generate Nonlocality Using Quantum Inputs.

Andrés F Ducuara1,2,3,4, Patryk Lipka-Bartosik5,6, Cristian E Susa7

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All incompatible measurement sets can generate quantum nonlocality when quantum inputs are used in an extended Bell scenario. This reveals hidden nonlocality, with extractable amounts limited by measurement incompatibility.

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Area of Science:

  • Quantum Information Theory
  • Foundations of Quantum Mechanics
  • Quantum Correlations

Background:

  • Bell nonlocality arises from incompatible measurements on spatially separated systems.
  • However, not all incompatible measurements yield Bell nonlocality; some produce only local correlations.

Purpose of the Study:

  • To demonstrate that all incompatible measurement sets can generate nonlocality.
  • To investigate the role of quantum inputs in revealing hidden nonlocality.
  • To establish an upper bound for extractable nonlocality.

Main Methods:

  • Introduction of a novel concept: generalized sets of measurements.
  • Analysis of Bell scenarios with quantum, rather than classical, measurement inputs.
  • Mathematical proof for the generation of nonlocality across all incompatible measurement sets.

Main Results:

  • All sets of incompatible measurements can generate nonlocality in an extended Bell scenario with quantum inputs.
  • Incompatible-local measurement sets exhibit a form of hidden nonlocality.
  • The maximum extractable nonlocality is bounded by the degree of measurement incompatibility.

Conclusions:

  • The extended Bell scenario with quantum inputs provides a universal framework for observing nonlocality.
  • This work unifies the study of different measurement scenarios and reveals inherent nonlocality in all incompatible sets.
  • A fundamental limit on extractable nonlocality is established, directly linked to measurement incompatibility.