Quantum dichotomies and coherent thermodynamics beyond first-order asymptotics

Abstract

We address the problem of exact and approximate transformation of quantum dichotomies in the asymptotic regime, i.e., the existence of a quantum channel $\mathcal{E}$ mapping ${\rho }_1^{\otimes n}$ into ${\rho }_2^{\otimes R_{n}n}$ with an error ${\epsilon }_n$ (measured by trace distance) and ${\sigma }_1^{\otimes n}$ into ${\sigma }_2^{\otimes R_{n}n}$ exactly, for a large number $n$. We derive second-order asymptotic expressions for the optimal transformation rate $R_n$ in the small, moderate, and large deviation error regimes, as well as the zero-error regime, for an arbitrary pair $({\rho }_1,{\sigma }_1)$ of initial states and a commuting pair $({\rho }_2,{\sigma }_2)$ of final states. We also prove that for ${\sigma }_1$ and ${\sigma }_2$ given by thermal Gibbs states, the derived optimal transformation rates in the first three regimes can be attained by thermal operations. This allows us, for the first time, to study the second-order asymptotics of thermodynamic state interconversion with fully general initial states that may have coherence between different energy eigenspaces. Thus, we discuss the optimal performance of thermodynamic protocols with coherent inputs and describe three novel resonance phenomena allowing one to significantly reduce transformation errors induced by finite-size effects. What is more, our result on quantum dichotomies can also be used to obtain, up to second-order asymptotic terms, optimal conversion rates between pure bipartite entangled states under local operations and classical communication.

53 pages, 6 figures, comments welcome

References in corpus (57)

• Advances in Quantum Metrology
• Quantifying Coherence
• Quantum metrology with nonclassical states of atomic ensembles
• Quantum Algorithms Revisited
• Conditions for a class of entanglement transformations
• Quantum Thermodynamics
• Quantum metrology from a quantum information science perspective
• Advances in Photonic Quantum Sensing
• Fundamental limitations for quantum and nano thermodynamics
• The elusive Heisenberg limit in quantum enhanced metrology
• On quantum Renyi entropies: a new generalization and some properties
• The second laws of quantum thermodynamics
• The Resource Theory of Quantum States Out of Thermal Equilibrium
• Fisher information and multiparticle entanglement
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Quantum coherence, time-translation symmetry and thermodynamics
• Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
• The resource theory of quantum reference frames: manipulations and monotones
• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• Quantum sensing with arbitrary frequency resolution
• A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
• Conditions for coherence transformations under incoherent operations
• An introductory review of the resource theory approach to thermodynamics
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
• Second-order asymptotics for quantum hypothesis testing
• Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
• Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
• alpha-z-relative Renyi entropies
• Gibbs-Preserving Maps outperform Thermal Operations in the quantum regime
• Energy Cost of Creating Quantum Coherence
• The second law of quantum thermodynamics as an equality
• Correlating thermal machines and the second law at the nanoscale
• Quantum work statistics close to equilibrium
• Comparison of quantum statistical models: equivalent conditions for sufficiency
• Hilbert's projective metric in quantum information theory
• Relative submajorization and its use in quantum resource theories
• Introducing one-shot work into fluctuation relations
• Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels
• Resource theory of asymmetric distinguishability
• Error exponents in hypothesis testing for correlated states on a spin chain
• Beyond the thermodynamic limit: finite-size corrections to state interconversion rates
• Moderate deviation analysis for classical communication over quantum channels
• An information-theoretic treatment of quantum dichotomies
• All states are universal catalysts in quantum thermodynamics
• Avoiding irreversibility: engineering resonant conversions of quantum resources
• Encoding classical information into quantum resources
• Comparison of Information Structures and Completely Positive Maps
• Quantum work statistics and resource theories: bridging the gap through Renyi divergences
• Strong Converse and Stein's Lemma in the Quantum Hypothesis Testing
• Two approaches to obtain the strong converse exponent of quantum hypothesis testing for general sequences of quantum states
• Fluctuation-dissipation relations for thermodynamic distillation processes
• Moderate deviation analysis of majorisation-based resource interconversion
• Geometric approach to quantum statistical inference
• Second law of thermodynamics for batteries with vacuum state
• Work and Fluctuations: Coherent vs. Incoherent Ergotropy Extraction
• Asymptotic majorization of finite probability distributions

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