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Local Randomness: Examples and Application.

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  • 1Joint Institute for Quantum Information and Computer Science, University of Maryland, College Park, MD, 20740.

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This summary is machine-generated.

Superclassical scores in nonlocal games guarantee intrinsic randomness. This study shows such scores also imply local randomness, crucial for quantum cryptography and secure tasks between mistrustful players.

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Area of Science:

  • Quantum Information Theory
  • Quantum Cryptography
  • Game Theory

Background:

  • Superclassical scores in nonlocal games necessitate intrinsic randomness in player outputs.
  • This intrinsic randomness has been recently shown to imply local randomness, where one player possesses randomness unknown to the other.
  • Local randomness has potential applications in cryptographic tasks involving cooperating but untrusting parties.

Purpose of the Study:

  • To advance the practical realization of local randomness.
  • To establish a near-optimal bound for local randomness in the CHSH game.
  • To demonstrate the security of a cryptographic application utilizing local randomness, specifically single-bit certified deletion.

Main Methods:

  • Analysis of nonlocal games and superclassical scores.
  • Derivation of bounds on local randomness for the CHSH game.
  • Security proof for the single-bit certified deletion protocol.

Main Results:

  • A near-optimal bound on local randomness for the CHSH game was established.
  • The security of the single-bit certified deletion protocol, based on local randomness, was proven.
  • The findings bridge theoretical concepts of quantum randomness with practical cryptographic applications.

Conclusions:

  • Superclassical scores in nonlocal games are a source of local randomness.
  • Local randomness offers a novel resource for quantum cryptography, particularly for tasks requiring conditional trust.
  • The study provides theoretical foundations and security guarantees for practical applications of local randomness.