Resource-Constrained Classical Communication

Abstract: Recently, new insights have been obtained by jointly studying classical communication and resource theory. This interplay consequently serves as a potential platform for interdisciplinary studies. To continue this line, we study non-signaling assisted classical communication scenarios constrained by a given resource, in the sense that the information processing channel is unable to supply additional amounts of the resource. The corresponding one-shot classical capacity is upper bounded by resource preservability, which is a measure of the ability to preserve the resource. A lower bound can be further obtained when the resource is asymmetry. As an application, unexpectedly, under a recently-studied thermalization model, we found that the smallest bath size needed to thermalize all outputs of a Gibbs-preserving coherence-annihilating channel upper bounds its non-signaling assisted one-shot classical capacity. This finding, therefore, bridges classical communication and thermodynamics. We also apply our approach to study how many pairs of orthogonal maximal entanglement can be maintained under channels constrained by different forms of inseparability. Our results demonstrate interdisciplinary applications enabled by dynamical resource theory.