Sufficient conditions for additivity of the zero-error classical capacity of quantum channels
Phys. Rev. A 114, 042447 – Published 22 October, 2026
DOI: https://doi.org/10.1103/1grz-q5np
Abstract
The one-shot zero-error classical capacity of a quantum channel is the maximum amount of classical information that can be transmitted with zero probability of error via a single channel use. This capacity is fundamentally characterized by the logarithm of the independence number of the noncommutative graph induced by the quantum channel. Consequently, the additivity of the one-shot zero-error classical capacity is equivalent to the multiplicativity of the independence number of the associated noncommutative graphs. As the independence number is not multiplicative in general, the specific conditions under which multiplicativity is preserved remain an open question in quantum information theory. Here, we establish some sufficient conditions for the multiplicativity of the independence number and provide explicit examples of quantum channels that satisfy these criteria. Furthermore, we investigate the block form of noncommutative graphs and derive conditions under which the independence number remains multiplicative within this framework. These results offer insights into the structural properties of noncommutative graphs and the fundamental limits of zero-error quantum communication.
