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Randomness in nonlocal games between mistrustful players.

Carl A Miller1, Yaoyun Shi2

  • 1National Institute of Standards and Technology, 100 Bureau Dr., Gaithersburg, MD 20890, USA, Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA.

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Achieving a superclassical score in nonlocal quantum games guarantees local randomness, meaning one player generates randomness independently of the other. This finding is crucial for device-independent quantum cryptography and secure communication protocols.

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Area of Science:

  • Quantum Information Theory
  • Quantum Cryptography
  • Game Theory

Background:

  • Device-independent quantum cryptography relies on superclassical scores in nonlocal games, implying randomness from an external observer's perspective.
  • The existence of local randomness (randomness held by only one player) in these scenarios has been an open question.

Purpose of the Study:

  • To determine if a superclassical score in a nonlocal game guarantees local randomness between quantum players.
  • To explore the implications of local randomness for quantum cryptographic protocols.

Main Methods:

  • Analysis of complete-support nonlocal games with quantum strategies.
  • Investigating player output recovery even when one player's input is known.

Main Results:

  • A superclassical score in complete-support games necessitates local randomness.
  • Even with knowledge of the other player's input, perfect output recovery is impossible, confirming local randomness.
  • Quantum strategies yield local randomness, unlike non-signaling strategies that may only produce global randomness.

Conclusions:

  • Superclassical scores in nonlocal games inherently generate local randomness, a key resource for quantum cryptography.
  • This local randomness is essential for building secure cryptographic protocols between mistrustful parties.