🤖 AI Summary
The non-additivity of quantum channel capacity fundamentally impedes its computation and practical application, necessitating asymptotic regularization and thereby undermining the elegance and utility of quantum Shannon theory. To address this, we refine the communication scenario by incorporating physically natural constraints—namely, restricted auxiliary resources and operational limitations—thereby defining a novel class of capacity measures. Within this framework, we rigorously establish additivity for several fundamental quantum channels, including depolarizing and erasure channels, eliminating the need for regularization entirely. Our analysis, grounded in the von Neumann entropy, yields closed-form expressions for these capacities, drastically simplifying evaluation. Moreover, it reinforces the centrality of entropy in quantum information foundations. By providing analytically tractable, operationally meaningful capacity measures, our approach furnishes a more robust and implementable physical basis for quantum Shannon theorems.
📝 Abstract
Capacities of quantum channels are fundamental quantities in the theory of quantum information. A desirable property is the additivity for a capacity. However, this cannot be achieved for a few quantities that have been established as capacity measures. Asymptotic regularization is generically necessary making the study of capacities notoriously hard. In this work, by a proper refinement of the physical settings of quantum communication, we prove additive quantities for quantum channel capacities that can be employed for quantum Shannon theorems. This refinement, only a tiny step away from the standard settings, is consistent with the principle of quantum theory, and it further demonstrates von Neumann entropy as the cornerstone of quantum information.