Application of the Resource Theory of Channels to Communication Scenarios

Abstract

We introduce a resource theory of channels relevant to communication via quantum channels, in which the set of constant channels --- useless channels for communication tasks --- is considered as the free resource. We find that our theory with such a simple structure is useful to address central problems in quantum Shannon theory --- in particular, we provide a converse bound for the one-shot non-signalling assisted classical capacity that naturally leads to its strong converse property, as well as obtain the one-shot channel simulation cost with non-signalling assistance. We clarify an intimate connection between the non-signalling assistance and our formalism by identifying the non-signalling assisted channel coding with the channel transformation under the maximal set of resource non-generating superchannels, providing a physical characterization of the latter. Our results provide new perspectives and concise arguments to those problems, connecting the recently developed fields of resource theories to `classic' settings in quantum information theory and shedding light on the validity of resource theories of channels as effective tools to address practical problems.

5+5 pages, 1 figure; published version

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• Physical Implementability of Linear Maps and Its Application in Error Mitigation
• Quantifying Quantumness of Channels Without Entanglement
• No-go theorems for quantum resource purification II: new approach and channel theory
• Universal and Operational Benchmarking of Quantum Memories
• Operational quantification of continuous-variable quantum resources
• One-Shot Manipulation of Dynamical Quantum Resources
• Resource Preservability
• Quantum Channel Marginal Problem
• Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps
• General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures
• Quantifying dynamical coherence with dynamical entanglement
• Symmetries of quantum evolutions
• Communication, Dynamical Resource Theory, and Thermodynamics
• Coherence of operations and interferometry
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• The Communication Value of a Quantum Channel
• Every quantum helps: Operational advantage of quantum resources beyond convexity
• Virtual quantum resource distillation: General framework and applications
• Characterisation of quantum betting tasks in terms of Arimoto mutual information
• Dynamical Landauer Principle: Quantifying Information Transmission by Thermodynamics
• Necessary and Sufficient Conditions on Measurements of Quantum Channels
• Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
• The Dynamical Resource Theory of Informational Non-Equilibrium
• Quantum Bell Nonlocality is Entanglement
• Resource Marginal Problems
• Quantum versus classical transport of energy in coupled two-level systems
• Quantum resource theory of coding for error correction
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• Reliable Simulation of Quantum Channels: the Error Exponent
• Quantifying entanglement preservability of experimental processes
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Black Box Work Extraction and Composite Hypothesis Testing
• One-shot manipulation of coherence in dynamic quantum resource theory
• Projective robustness for quantum channels and measurements and their operational significance
• Informational non-equilibrium concentration
• Postselected communication over quantum channels
• Improving quantum channel discrimination with resourceful states
• Quantum correlation generation capability of experimental processes
• Mixed-permutation channel with its application to estimate quantum coherence
• Resource theory of interactive quantum instruments
• Entropic and operational characterizations of dynamic quantum resources
• Thermodynamic criteria for signaling in quantum channels
• Complete characterisation of state conversions by work extraction
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• Retrocausal capacity of a quantum channel: Communicating through noisy closed timelike curves