AI summaryⓘ
The authors study how quantum channels, which process quantum information, can be understood as resources for thermodynamics when assisted by memory-like side channels. They focus on a special framework called conditional athermality, deriving how efficiently one can convert between channels and identity operations while preserving certain thermal properties. Their results link these efficiencies to a concept called conditional channel entropy, highlighting how signaling affects quantum processes. They also prove that for certain types of channels, this resource theory is reversible, meaning no resource is lost when converting back and forth in the long run. Overall, they present conditional channel entropy as a fundamental tool for understanding quantum information thermodynamics.
Quantum channelResource theoryAthermalityConditional entropyGibbs-preserving mapOne-shot rateTele-covariant channelNo-signalingAsymptotic reversibilitySuperdense coding
Authors
Himanshu Badhani, Siddhartha Das
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.