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This study explores quantum communication limits using photon-number statistics for device certification. The developed method improves semi-device-independent random number generation protocols.

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Area of Science:

  • Quantum Information Science
  • Quantum Communication Security

Background:

  • Quantum communication protocols often face practical constraints, such as photon-number statistics in optical systems.
  • Semi-device-independent (SDI) certification offers a robust security framework but requires careful analysis of these constraints.

Purpose of the Study:

  • To develop a method for bounding quantum correlations under photon-number distribution restrictions.
  • To apply this method for certifying SDI random number generation (RNG) protocols and enhancing randomness extraction.

Main Methods:

  • Utilized semidefinite programming (SDP) relaxations for noncommutative polynomial optimization.
  • Analyzed quantum correlations within the prepare-and-measure scenario with photon-number constraints.
  • Applied the method to bound conditional Shannon entropy in SDI-RNG protocols.

Main Results:

  • Established a technique to bound quantum correlations restricted by photon-number distributions.
  • Demonstrated the method's practicality by computing performance bounds for communication tasks.
  • Successfully bounded conditional Shannon entropy for SDI-RNG protocols.

Conclusions:

  • The SDP-based approach provides a versatile tool for analyzing quantum correlations under practical constraints.
  • This method enhances randomness extraction in established SDI-RNG protocols, particularly those using coherent states and homodyne measurements.