Erasing, Converting, and Communicating: The Power of Resource-Nongenerating Operations

Abstract: We investigate resource nongenerating operations (RNOs) in both static and dynamical quantum resource theories. For the static scenarios, we derive a sufficient condition for state transformations under RNOs. Then we construct a dynamical resource theory where RNOs constitute the set of free operations, and we propose an axiomatic approach to quantify quantum channels. We further analyze the erasure of the dynamical resources. As applications, we establish bounds on the asymptotic cost of states under RNOs in a generic convex resource theory and obtain capacity bounds for communication tasks assisted by dynamical coherence. Our results clarify the key roles of RNOs in quantum information processing tasks.