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Duality Games and Operational Duality Relations.

Emilio Bagan1, John Calsamiglia1, János A Bergou2,3

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Wave-particle duality is operationalized using discrimination games, where winning probabilities are constrained. A new duality relation bounds the probability of winning combined games, linking duality to discrimination probabilities.

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Area of Science:

  • Quantum mechanics
  • Quantum information theory

Background:

  • Wave-particle duality is a fundamental concept in quantum mechanics.
  • Operational definitions are crucial for understanding quantum phenomena.

Purpose of the Study:

  • To provide an operational meaning to wave-particle duality.
  • To establish a quantitative relationship between wave-particle duality and discrimination games.

Main Methods:

  • Utilizing an n-port interferometer for discrimination games.
  • Involving three parties: Alice and Bob (cooperating) and the House (supervising).
  • Defining two games: 'ways' (path determination) and 'phases' (phase determination).

Main Results:

  • A tight wave-particle duality relation was derived.
  • This relation connects the probabilities of winning the 'ways' and 'phases' games.
  • An upper bound for the probability of winning the combined game was established.

Conclusions:

  • Wave-particle duality can be expressed in terms of discrimination probabilities.
  • The study offers a novel operational framework for wave-particle duality.