Computing Classical-Quantum Channel Capacity Using Blahut–Arimoto Type Algorithm: A Theoretical and Numerical Analysis †
| Autor: | Ning Cai, Haobo Li |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Blahut–Arimoto type algorithm
Kullback–Leibler divergence Iterative method General Physics and Astronomy lcsh:Astrophysics 02 engineering and technology Type (model theory) 01 natural sciences convergence speed Article Dimension (vector space) 0103 physical sciences lcsh:QB460-466 0202 electrical engineering electronic engineering information engineering 010306 general physics lcsh:Science Mathematics capacity 020206 networking & telecommunications State (functional analysis) Binary logarithm lcsh:QC1-999 TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Bounded function classical-quantum channel lcsh:Q Linear independence Algorithm lcsh:Physics |
| Zdroj: | Entropy Volume 22 Issue 2 Entropy, Vol 22, Iss 2, p 222 (2020) |
| ISSN: | 1099-4300 |
| Popis: | Based on Arimoto&rsquo s work in 1972, we propose an iterative algorithm for computing the capacity of a discrete memoryless classical-quantum channel with a finite input alphabet and a finite dimensional output, which we call the Blahut&ndash Arimoto algorithm for classical-quantum channel, and an input cost constraint is considered. We show that, to reach &epsilon accuracy, the iteration complexity of the algorithm is upper bounded by log n log &epsilon &epsilon where n is the size of the input alphabet. In particular, when the output state { &rho x } x &isin X is linearly independent in complex matrix space, the algorithm has a geometric convergence. We also show that the algorithm reaches an &epsilon accurate solution with a complexity of O ( m 3 log n log &epsilon ) , and O ( m 3 log &epsilon log ( 1 - &delta ) &epsilon D ( p * | | p N 0 ) ) in the special case, where m is the output dimension, D ( p * | | p N 0 ) is the relative entropy of two distributions,, and &delta is a positive number. Numerical experiments were performed and an approximate solution for the binary two-dimensional case was analysed. |
| Databáze: | OpenAIRE |
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