Thermodynamic Implementations of Quantum Processes

Abstract

Recent understanding of the thermodynamics of small-scale systems have enabled the characterization of the thermodynamic requirements of implementing quantum processes for fixed input states. Here, we extend these results to construct optimal universal implementations of a given process, that is, implementations that are accurate for any possible input state even after many independent and identically distributed (i.i.d.) repetitions of the process. We find that the optimal work cost rate of such an implementation is given by the thermodynamic capacity of the process, which is a single-letter and additive quantity defined as the maximal difference in relative entropy to the thermal state between the input and the output of the channel. As related results we find a new single-shot implementation of time-covariant processes and conditional erasure with nontrivial Hamiltonians, a new proof of the asymptotic equipartition property of the coherent relative entropy, and an optimal implementation of any i.i.d. process with thermal operations for a fixed i.i.d. input state. Beyond being a thermodynamic analogue of the reverse Shannon theorem for quantum channels, our results introduce a new notion of quantum typicality and present a thermodynamic application of convex-split methods.

arXiv comment46+15 pages, 2 figures. The appendix of arXiv:1807.05610 was split off and reworked into this technical companion paper. Version v2 reflects the journal accepted version but is extended with some additional related results (Section 8) that are not included in the published work

References in corpus (48)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Quantum Resource Theories
• The role of quantum information in thermodynamics --- a topical review
• The Uncertainty Principle in the Presence of Quantum Memory
• Fundamental limitations for quantum and nano thermodynamics
• The second laws of quantum thermodynamics
• The Resource Theory of Quantum States Out of Thermal Equilibrium
• 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 Sharp Fannes-type Inequality for the von Neumann Entropy
• A Fully Quantum Asymptotic Equipartition Property
• A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
• Truly work-like work extraction
• Duality Between Smooth Min- and Max-Entropies
• Quantum Reverse Shannon Theorem
• Optimal Cloning of Pure States, Judging Single Clones
• 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
• The Minimal Work Cost of Information Processing
• Gibbs-Preserving Maps outperform Thermal Operations in the quantum regime
• Finite blocklength converse bounds for quantum channels
• Resource Theory of Coherence - Beyond States
• How to quantify a dynamical quantum resource
• One shot entanglement assisted classical and quantum communication over noisy quantum channels: A hypothesis testing and convex split approach
• Quantum message compression with applications
• Multiplicativity of completely bounded p-norms implies a new additivity result
• Approximate reversibility in the context of entropy gain, information gain, and complete positivity
• Quantum Channel Simulation and the Channel's Smooth Max-Information
• Generalized Entropies
• Thermodynamic Capacity of Quantum Processes
• 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
• The entropy gain of infinite-dimensional quantum channels
• Computing Quantum Channel Capacities
• "Pretty strong" converse for the quantum capacity of degradable channels
• Disentanglement Cost of Quantum States
• A generalized quantum Slepian-Wolf
• Partially smoothed information measures
• Convex-split and hypothesis testing approach to one-shot quantum measurement compression and randomness extraction
• On simultaneous min-entropy smoothing
• A one-shot achievability result for quantum state redistribution
• A minimax approach to one-shot entropy inequalities
• Non-thermal quantum channels as a thermodynamical resource

Cited by in corpus (9)

• Reassessing thermodynamic advantage from indefinite causal order
• Quantum processes as thermodynamic resources: the role of non-Markovianity
• Asymptotic Reversibility of Thermal Operations for Interacting Quantum Spin Systems via Generalized Quantum Stein's Lemma
• Reliable Simulation of Quantum Channels: the Error Exponent
• Gibbs-preserving operations requiring infinite amount of quantum coherence
• Reliability Function of Quantum Information Decoupling via the Sandwiched Rényi Divergence
• Thermodynamic state convertibility is determined by qubit cooling and heating
• Thermodynamic criteria for signaling in quantum channels
• Strong symmetries in collision models and physical dilations of covariant quantum maps