Related papers: Sufficient conditions for additivity of the zero-error classical capacity of quantum channels

Sufficient conditions for additivity of the zero-error classical capacity of quantum channels

URL: http://arxiv.org/abs/2601.18538v1
Date: Mon, 26 Jan 2026 14:45:23 GMT
Title: Sufficient conditions for additivity of the zero-error classical capacity of quantum channels
Authors: Jeonghoon Park, Jeong San Kim,
Abstract summary: The one-shot zero-error classical capacity of a quantum channel is equivalent to the multiplicativity of the independence number of the noncommutative graph.<n>We consider a block form of noncommutative graphs, and provide conditions when the independence number is multiplicative.
Score: 2.733522537300566
License: http://creativecommons.org/licenses/by-nc-sa/4.0/
Abstract: The one-shot zero-error classical capacity of a quantum channel is the amount of classical information that can be transmitted with zero probability of error by a single use. Then the one-shot zero-error classical capacity equals to the logarithmic value of the independence number of the noncommutative graph induced by the channel. Thus the additivity of the one-shot zero-error classical capacity of a quantum channel is equivalent to the multiplicativity of the independence number of the noncommutative graph. The independence number is not multiplicative in general, and it is not clearly understood when the multiplicativity occurs. In this work, we present sufficient conditions for multiplicativity of the independence number, and we give explicit examples of quantum channels. Furthermore, we consider a block form of noncommutative graphs, and provide conditions when the independence number is multiplicative.

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