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Reliability Function of Classical-Quantum Channels.

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This study establishes a lower bound for the reliability function in classical-quantum channels, resolving a 20-year-old conjecture in quantum information theory. The findings determine the reliability function for high-rate communication. Keywords: quantum information theory, classical-quantum channels, reliability function.

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Area of Science:

  • Quantum Information Theory
  • Quantum Communication
  • Channel Coding

Background:

  • The reliability function quantifies error decay in classical-quantum channels below capacity.
  • Holevo's conjecture (2000) proposed a bound for this function, remaining an open problem.
  • Existing upper bounds by Dalai (2013) provided insights for high-rate communication.

Purpose of the Study:

  • To establish a lower bound for the reliability function of general classical-quantum channels.
  • To resolve Holevo's conjecture on the reliability function.
  • To determine the reliability function in the high-rate communication regime.

Main Methods:

  • Utilizing quantum Rényi information in Petz's form to derive a lower bound.
  • Building upon Renes' (2022) work connecting channel coding and privacy amplification.
  • Developing a new characterization of channel Rényi information.

Main Results:

  • A novel lower bound for the reliability function is proven.
  • Holevo's conjecture is resolved, a significant advancement in quantum information theory.
  • The derived lower bound matches Dalai's upper bound at high communication rates, determining the reliability function in this regime.

Conclusions:

  • The reliability function for classical-quantum channels is now better understood, particularly at high rates.
  • The resolution of Holevo's conjecture opens new avenues for research in quantum communication.
  • The study provides a complete characterization of the reliability function under specific conditions.