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Joint Probabilities Approach to Quantum Games with Noise.

Alexis R Legón1,2, Ernesto Medina2,3

  • 1Departamento de Física, Universidad Técnica Federico Santa María, Av. España 1680, Casilla 110 V, Valparaíso 2390123, Chile.

Entropy (Basel, Switzerland)
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Noise in quantum games does not destroy entanglement. A new formalism shows that while noise affects game strategies, entanglement is preserved, offering insights into quantum correlations.

Keywords:
correlation measuredilemma dissolutionnoisequantum gamesquantum strategies

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Area of Science:

  • Quantum Information Theory
  • Game Theory
  • Quantum Computing

Background:

  • Quantum games extend classical game theory by incorporating quantum mechanics principles.
  • Noise is a critical factor in quantum systems, potentially affecting quantum correlations and game outcomes.
  • Non-factorizable probabilities offer a framework to analyze joint probabilities in complex quantum scenarios.

Purpose of the Study:

  • To propose a joint probability formalism for quantum games with noise.
  • To investigate the impact of noise on entanglement and Nash inequalities in various quantum games.
  • To develop a new correlation measure for classical and quantum strategies under noise.

Main Methods:

  • Developed a joint probability formalism inspired by non-factorizable probabilities.
  • Applied the formalism to analyze the Prisoner's Dilemma, Chicken Game, and Battle of the Sexes with a single noise parameter (μ).
  • Introduced and analyzed a new correlation measure for classical and quantum strategies.

Main Results:

  • Demonstrated that noise does not generically destroy entanglement in quantum games.
  • Identified a threshold for noise beyond which Nash inequalities fail for most games, except the Battle of the Sexes.
  • Showcased that classical strategies can approximate quantum game behavior with noise, preserving correlations.

Conclusions:

  • The proposed formalism effectively models noise in quantum games, confirming entanglement's resilience.
  • Noise impacts strategic inequalities differently across games, with the Battle of the Sexes being noise-resilient.
  • The new correlation measure highlights how noise can enhance classical strategy performance, mimicking quantum effects.