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Violating any two-input Bell inequality is necessary and sufficient for certifying quantum randomness. However, this sufficiency is lost for multiple-input inequalities, impacting device-independent random number generation.

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Area of Science:

  • Quantum Information Science
  • Foundations of Quantum Mechanics

Background:

  • Device-independent randomness certification relies on Bell nonlocality for security.
  • The minimal resource requirements for nonlocality-based randomness generation remain unclear.

Purpose of the Study:

  • To clarify the minimal resource requirements for certifying randomness via Bell nonlocality.
  • To investigate the relationship between Bell inequality violations and randomness certification in multi-input scenarios.

Main Methods:

  • Theoretical proof of necessity and sufficiency for two-input Bell inequalities.
  • Experimental demonstration using high-dimensional photonic systems.
  • Analysis of facet inequalities and Salavrakos-Augusiak-Tura-Wittek-Acín-Pironio inequalities.

Main Results:

  • Violation of any two-input Bell inequality is proven necessary and sufficient for randomness certification.
  • Sufficiency is lost for multiple-input Bell inequalities, where Bell nonlocality does not guarantee randomness.
  • The Salavrakos-Augusiak-Tura-Wittek-Acín-Pironio inequalities were shown to always certify randomness, unlike facet inequalities.
  • A private randomness generation rate of 1.867±0.018 bits per photon pair was achieved.

Conclusions:

  • Establishes a precise link between Bell nonlocality and randomness certification.
  • Identifies specific Bell inequalities suitable for device-independent randomness generation.
  • Enhances the performance and security of device-independent random number generation.