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Machine Learning: Information TheoryCognitive Modeling & Cognitive Systems: Neural Spike CodingReasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
Conditional channel entropy sets fundamental limits on thermodynamic quantum information processing
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This work investigates the thermodynamic information-processing capabilities of bipartite quantum channels within the resource theory of conditional athermality and their interplay with causal structure and quantum correlations. By introducing an auxiliary memory channel, the study endows conditional channel entropy with its first operational meaning, characterizing the optimal one-shot rates for identity channel distillation and simulation, and revealing a direct trade-off with quantum signal transmission. Leveraging tools such as conditional Gibbs-preserving superchannels, conditional min-entropy, and Choi-state analysis, the authors prove that the asymptotic conditional athermality capacity of teleportation-covariant channels equals half the superdense coding capacity of their Choi states. This establishes conditional channel entropy as a fundamental measure of quantum processes and demonstrates asymptotic reversibility for specific classes of channels.
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📝 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.
Problem
Research questions and friction points this paper is trying to address.
conditional channel entropy
thermodynamic quantum information processing
quantum correlations
resource theory of athermality
quantum channels
Innovation
Methods, ideas, or system contributions that make the work stand out.
conditional channel entropy
resource theory of athermality
quantum thermodynamics
tele-covariant channels
asymptotic reversibility
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2023-11-17Citations: 2
