Gibbs-preserving operations requiring infinite amount of quantum coherence

Abstract

Gibbs-preserving operations have been studied as one of the standard free processes in quantum thermodynamics. Although they admit a simple mathematical structure, their operational significance has been unclear due to the potential hidden cost to implement them using an operatioanlly motivated class of operations, such as thermal operations. Here, we show that this hidden cost can be infinite -- we present a family of Gibbs-preserving operations that cannot be implemented by thermal operations aided by any finite amount of quantum coherence. Our result implies that there are uncountably many Gibbs-preserving operations that require unbounded thermodynamic resources to implement, raising a question about employing Gibbs-preserving operations as available thermodynamics processes. This finding is a consequence of the general lower bounds we provide for the coherence cost of approximately implementing a certain class of Gibbs-preserving operations with a desired accuracy. We find that our lower bound is almost tight, identifying a quantity -- related to the energy change caused by the channel to implement -- as a fundamental quantifier characterizing the coherence cost for the approximate implementation of Gibbs-preserving operations.

29(7+22) pages, 1 figure, accepted in PRL

References in corpus (47)

• Quantum entanglement
• Black holes as mirrors: quantum information in random subsystems
• Quantum Resource Theories
• The second laws of quantum thermodynamics
• Distance measures to compare real and ideal quantum processes
• The Resource Theory of Quantum States Out of Thermal Equilibrium
• Min- and Max- Relative Entropies and a New Entanglement Monotone
• Quantum coherence, time-translation symmetry and thermodynamics
• Restrictions on Transversal Encoded Quantum Gate Sets
• Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
• The resource theory of quantum reference frames: manipulations and monotones
• The thermodynamic meaning of negative entropy
• Reversible transformations from pure to mixed states, and the unique measure of information
• Optimal Cloning of Pure States, Judging Single Clones
• An introductory review of the resource theory approach to thermodynamics
• 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
• A general framework for quantum macroscopicity in terms of coherence
• One-Shot Operational Quantum Resource Theory
• Convex geometry of quantum resource quantification
• A reversible theory of entanglement and its relation to the second law
• Conservative Quantum Computing
• Clock-work trade-off relation for coherence in quantum thermodynamics
• Benchmarking one-shot distillation in general quantum resource theories
• Conservation laws, uncertainty relations, and quantum limits of measurements
• Quantum thermodynamics of correlated-catalytic state conversion at small-scale
• Resource theory of asymmetric distinguishability
• Skew informations from an operational view via resource theory of asymmetry
• Detecting metrologically useful asymmetry and entanglement by a few local measurements
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem
• Thermodynamic Capacity of Quantum Processes
• Fundamental work cost of quantum processes
• Uncertainty relations in implementation of unitary operations
• New perspectives on covariant quantum error correction
• Work Cost of Thermal Operations in Quantum and Nano Thermodynamics
• An information-theoretic treatment of quantum dichotomies
• One-shot entanglement distillation beyond local operations and classical communication
• Optimal Universal Quantum Error Correction via Bounded Reference Frames
• Coherence cost for violating conservation laws
• Correlations in typicality and an affirmative solution to the exact catalytic entropy conjecture
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
• Wigner-Araki-Yanase theorem for continuous and unbounded conserved observables
• Thermodynamic Implementations of Quantum Processes
• Fisher information matrix as a resource measure in resource theory of asymmetry with general connected Lie group symmetry
• Smooth Metric Adjusted Skew Information Rates
• Beyond i.i.d. in the Resource Theory of Asymmetry: An Information-Spectrum Approach for Quantum Fisher Information

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