Conditional channel entropy sets fundamental limits on thermodynamic quantum information processing

TL;DR

This paper introduces the concept of conditional channel entropy in quantum information, linking it to thermodynamic limits and operational tasks like channel simulation and capacity, especially in the presence of memory effects.

Contribution

It characterizes the operational significance of conditional channel entropies and establishes their role in the resource theory of athermality for quantum channels with memory.

Findings

Optimal one-shot rates for channel distillation and simulation are characterized.

Conditional channel min-entropy exhibits an equipartition property for certain classes of channels.

Asymptotic reversibility of the resource theory is demonstrated for tele-covariant and no-signaling channels.

Abstract

The thermodynamic resourcefulness of quantum channels primarily depends on their underlying causal structure and their ability to generate quantum correlations. We quantify this interplay within the resource theory of athermality for bipartite quantum channels in the presence of a side channel acting as memory, referred to as the resource theory of conditional athermality. For channels with trivial output Hamiltonians, we characterize the optimal one-shot rates for distilling the identity gate from a given channel, as well as the cost of simulating the channel using the identity gate, under conditional Gibbs-preserving superchannels. We show that these rates have a direct trade-off relation with the conditional channel entropies, attributing operational significance to signaling in quantum processes. Furthermore, we establish an equipartition property for the conditional channel min-entropy for classes of channels that are either tele-covariant or no-signaling from the non-conditioning input to the conditioning output. As a consequence, we demonstrate asymptotic reversibility of the resource theory for these channels. The asymptotic conditional athermality capacity of a tele-covariant channel is half the superdense coding capacity of its Choi state. Our work establishes the conditional channel entropy as a primitive information-theoretic concept for quantum processes, elucidating its potential for wider applications in quantum information science.