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Optimal and Feasible Contextuality-Based Randomness Generation.

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Semi-device-independent randomness generation using Kochen-Specker contextuality offers practical advantages. This study introduces new methods for optimal randomness certification and relaxes assumptions, enhancing security and applicability for quantum information processing.

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Area of Science:

  • Quantum Information Science
  • Quantum Foundations
  • Quantum Cryptography

Background:

  • Semi-device-independent (SDT) randomness generation protocols leverage Kochen-Specker contextuality.
  • These protocols offer advantages over fully device-independent (DI) protocols, including compact devices, high rates, and experimental simplicity.
  • A key assumption is the repeatability of measurements and adherence to an intended compatibility structure.

Purpose of the Study:

  • To improve the state-of-the-art in semi-device-independent randomness generation.
  • To introduce new experimentally feasible structures for optimal randomness certification.
  • To relax existing assumptions and analyze security against broader classes of adversaries.

Main Methods:

  • Introduction of a family of simple, experimentally feasible orthogonality graphs (measurement compatibility structures).
  • Analytical derivation of the Lovász theta and fractional packing number for these graphs.
  • Framing relaxation of measurement compatibility in terms of ϵ-orthogonality graphs and deriving corresponding quantum correlations.

Main Results:

  • Demonstrated that specific orthogonality graphs allow certification of the maximum log₂d bits of randomness from qudit systems (d≥3).
  • Proved the utility of these graphs for optimal randomness expansion and amplification.
  • Derived quantum correlations enabling randomness certification for arbitrary relaxation ϵ∈[0,1) of measurement compatibility.
  • Showed that single-qubit correlations can be almost contextual, resisting ϵ-faithful noncontextual hidden variable models for small ϵ.
  • Identified potential security vulnerabilities against quantum and consistent adversaries.

Conclusions:

  • The developed orthogonality graphs are optimal for randomness generation in the semi-device-independent setting.
  • The relaxation of measurement compatibility broadens the applicability of contextuality-based randomness generation.
  • Single qubits exhibit near-contextual behavior, with implications for quantum foundations.
  • Security analysis against a wider range of adversaries is crucial for robust quantum protocols.