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Computing Classical-Quantum Channel Capacity Using Blahut-Arimoto Type Algorithm: A Theoretical and Numerical

Haobo Li1,2,3, Ning Cai1

  • 1School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

We developed the Blahut-Arimoto algorithm to calculate classical-quantum channel capacity under input cost constraints. This iterative method offers efficient computation with proven iteration complexity bounds for achieving accurate results.

Keywords:
Blahut–Arimoto type algorithmcapacityclassical-quantum channelconvergence speed

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Area of Science:

  • Quantum Information Theory
  • Classical-Quantum Channels
  • Information Theory

Background:

  • The capacity of classical-quantum channels is crucial for quantum communication.
  • Existing methods for capacity calculation can be computationally intensive.
  • Arimoto's work laid the foundation for iterative capacity computation.

Purpose of the Study:

  • To propose an iterative algorithm for computing the capacity of discrete memoryless classical-quantum channels.
  • To analyze the algorithm's performance under input cost constraints.
  • To provide theoretical bounds on iteration complexity and convergence rates.

Main Methods:

  • The Blahut-Arimoto algorithm for classical-quantum channels is introduced.
  • Iteration complexity is analyzed with respect to input alphabet size (n) and accuracy (ε).
  • Convergence properties are studied, including geometric convergence under specific conditions.

Main Results:

  • The algorithm's iteration complexity is upper bounded by log(n)log(ε)/ε.
  • Geometric convergence is achieved when output states are linearly independent.
  • An ε-accurate solution is reached with complexity O(m³ log(n)log(ε)/ε).

Conclusions:

  • The Blahut-Arimoto algorithm provides an efficient method for calculating classical-quantum channel capacity.
  • The algorithm demonstrates favorable complexity and convergence properties.
  • Numerical experiments validate the algorithm's applicability, particularly in the binary two-dimensional case.