Thermodynamic Capacity of Quantum Processes

Abstract

Thermodynamics imposes restrictions on what state transformations are possible. In the macroscopic limit of asymptotically many independent copies of a state---as for instance in the case of an ideal gas---the possible transformations become reversible and are fully characterized by the free energy. In this Letter, we present a thermodynamic resource theory for quantum processes that also becomes reversible in the macroscopic limit, a property that is especially rare for a resource theory of quantum channels. We identify a unique single-letter and additive quantity, the thermodynamic capacity, that characterizes the "thermodynamic value" of a quantum channel, in the sense that the work required to simulate many repetitions of a quantum process employing many repetitions of another quantum process becomes equal to the difference of the respective thermodynamic capacities. On a technical level, we provide asymptotically optimal constructions of universal implementations of quantum processes. A challenging aspect of this construction is the apparent necessity to coherently combine thermal engines that would run in different thermodynamic regimes depending on the input state. Our results have applications in quantum Shannon theory by providing a generalized notion of quantum typical subspaces and by giving an operational interpretation to the entropy difference of a channel.

arXiv comment6 pages, 2 figures, journal version. The technical appendix was split off into a companion paper that will be submitted separately (cf. today's arXiv listing)

References in corpus (48)

• Concentrating Partial Entanglement by Local Operations
• Quantum Resource Theories
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Fundamental limitations for quantum and nano thermodynamics
• The second laws of quantum thermodynamics
• The Resource Theory of Quantum States Out of Thermal Equilibrium
• Catalytic Coherence
• Min- and Max- Relative Entropies and a New Entanglement Monotone
• Quantum coherence, time-translation symmetry and thermodynamics
• Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
• The thermodynamic meaning of negative entropy
• Post-selection technique for quantum channels with applications to quantum cryptography
• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• One-Shot Classical-Quantum Capacity and Hypothesis Testing
• A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
• Quantum Reverse Shannon Theorem
• The quantum capacity of channels with arbitrarily correlated noise
• The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
• Sample-optimal tomography of quantum states
• Memory effects in quantum channel discrimination
• The Minimal Work Cost of Information Processing
• Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
• Gibbs-Preserving Maps outperform Thermal Operations in the quantum regime
• Finite blocklength converse bounds for quantum channels
• Universal Quantum Information Compression
• One shot entanglement assisted classical and quantum communication over noisy quantum channels: A hypothesis testing and convex split approach
• Quantum universal variable-length source coding
• Quantum message compression with applications
• Multiplicativity of completely bounded p-norms implies a new additivity result
• Applications of coherent classical communication and the Schur transform to quantum information theory
• The asymmetry properties of pure quantum states
• Approximate reversibility in the context of entropy gain, information gain, and complete positivity
• Generalized Entropies
• Fundamental work cost of quantum processes
• Beyond the thermodynamic limit: finite-size corrections to state interconversion rates
• Catalytic Decoupling of Quantum Information
• Identifying the Information Gain of a Quantum Measurement
• Resource theories of quantum channels and the universal role of resource erasure
• Amortized entanglement of a quantum channel and approximately teleportation-simulable channels
• Universal quantum data compression via gentle tomography
• The entropy gain of infinite-dimensional quantum channels
• "Pretty strong" converse for the quantum capacity of degradable channels
• A generalized quantum Slepian-Wolf
• A one-shot achievability result for quantum state redistribution
• Non-thermal quantum channels as a thermodynamical resource
• Multiparty quantum protocols for assisted entanglement distillation
• Global and local gauge symmetries beyond Lagrangian formulations
• Unions, intersections and a one-shot quantum joint typicality lemma

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• Entanglement cost and quantum channel simulation
• Work extraction processes from noisy quantum batteries: the role of non local resources
• On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources
• Fundamental limitations on photoisomerization from thermodynamic resource theories
• Computing Quantum Channel Capacities
• Coherence cost for violating conservation laws
• Quantum work extraction efficiency for noisy quantum batteries: the role of coherence
• Partially smoothed information measures
• The nonequilibrium cost of accurate information processing
• Convex-split and hypothesis testing approach to one-shot quantum measurement compression and randomness extraction
• Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes
• Reassessing thermodynamic advantage from indefinite causal order
• Partial order on passive states and Hoffman majorization in quantum thermodynamics
• Necessary and Sufficient Conditions on Measurements of Quantum Channels
• The Dynamical Resource Theory of Informational Non-Equilibrium
• Thermodynamic Implementations of Quantum Processes
• Overcoming entropic limitations on asymptotic state transformations through probabilistic protocols
• Channels, measurements and post-selection in quantum thermodynamics
• Asymptotic Reversibility of Thermal Operations for Interacting Quantum Spin Systems via Generalized Quantum Stein's Lemma
• Quantum processes as thermodynamic resources: the role of non-Markovianity
• Quantum and classical dynamical semigroups of superchannels and semicausal channels
• DQC1 as an Open Quantum System
• Reliable Simulation of Quantum Channels: the Error Exponent
• Gibbs-preserving operations requiring infinite amount of quantum coherence
• Relations between Markovian and non-Markovian correlations in multitime quantum processes
• Black Box Work Extraction and Composite Hypothesis Testing
• Magnonic Thermal Machines
• Quantum thermodynamics with coherence: Covariant Gibbs-preserving operation is characterized by the free energy
• Thermodynamic state convertibility is determined by qubit cooling and heating
• Towards the ultimate limits of quantum channel discrimination and quantum communication
• Classical communication cost of a bipartite quantum channel assisted by non-signalling correlations
• Universal work extraction in quantum thermodynamics
• Preprocessing operations and the reverse compression