How to quantify a dynamical quantum resource

Abstract

We show that the generalization of the relative entropy of a resource from states to channels is not unique, and there are at least six such generalizations. We then show that two of these generalizations are asymptotically continuous, satisfy a version of the asymptotic equipartition property, and their regularizations appear in the power exponent of channel versions of the quantum Stein's Lemma. To obtain our results, we use a new type of "smoothing" that can be applied to functions of channels (with no state analog). We call it "liberal smoothing" as it allows for more spread in the optimization. Along the way, we show that the diamond norm can be expressed as a D_max distance to the set of quantum channels, and prove a variety of properties of all six generalizations of the relative entropy of a resource.

arXiv comment5 pages (main text) + 20 pages (appendix), references added, published version

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Cited by in corpus (64)

• Operational Resource Theory of Quantum Channels
• No-Go Theorems for Quantum Resource Purification
• On the Role of Coherence in Shor's Algorithm
• Dynamical Resource Theory of Quantum Coherence
• Dynamical Entanglement
• Entanglement of a bipartite channel
• Fundamental limitations on distillation of quantum channel resources
• On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources
• Experimental quantification of coherence of a tunable quantum detector
• One-Shot Manipulation of Dynamical Quantum Resources
• Tight constraints on probabilistic convertibility of quantum states
• Resource Preservability
• 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
• Resource theory of quantum uncomplexity
• Quantifying dynamical coherence with dynamical entanglement
• Symmetries of quantum evolutions
• Communication, Dynamical Resource Theory, and Thermodynamics
• Quantifying dynamical magic with completely stabilizer preserving operations as free
• Coherence of operations and interferometry
• Relation between Quantum Coherence and Quantum Entanglement in Quantum Measurements
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Monotones in General Resource Theories
• Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes
• Every quantum helps: Operational advantage of quantum resources beyond convexity
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
• Accessible coherence in open quantum system dynamics
• Virtual quantum resource distillation: General framework and applications
• Uniqueness and Optimality of Dynamical Extensions of Divergences
• Incompatibility as a resource for programmable quantum instruments
• Necessary and Sufficient Conditions on Measurements of Quantum Channels
• Entanglement-breaking superchannels
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• Thermodynamic Implementations of Quantum Processes
• Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
• One-shot manipulation of entanglement for quantum channels
• Quantum Bell Nonlocality is Entanglement
• Resource theory of heat and work with non-commuting charges
• Entanglement resource theory of quantum channel
• Universal construction of decoders from encoding black boxes
• Resource Marginal Problems
• What is Entropy? A new perspective from games of chance
• Compositional resource theories of coherence
• Quantum Network Discrimination
• Quantifying entanglement preservability of experimental processes
• Computable lower bounds on the entanglement cost of quantum channels
• Black Box Work Extraction and Composite Hypothesis Testing
• From Quantum Source Compression to Quantum Thermodynamics
• One-shot manipulation of coherence in dynamic quantum resource theory
• Covariant influences for finite discrete dynamical systems
• On coherence of quantum operations by using Choi-Jamiołkowski isomorphism
• Projective robustness for quantum channels and measurements and their operational significance
• One-Shot Static Entanglement Cost of Bipartite Quantum Channels
• Towards the ultimate limits of quantum channel discrimination and quantum communication
• Process tensor distinguishability measures
• Single-shot entanglement manipulation of states and channels revisited
• Entropic and operational characterizations of dynamic quantum resources
• Quantum Dynamical Resource Theory under Resource Non-increasing Framework
• Quantum correlation generation capability of experimental processes
• Classical communication cost of a bipartite quantum channel assisted by non-signalling correlations
• The entropy of quantum causal networks
• Quantifying Dynamical Total Coherence in a Resource Non-increasing Framework
• Quantifying coherence of quantum measurements
• Macroscopicity and observational deficit in states, operations, and correlations