All states are universal catalysts in quantum thermodynamics

Abstract

Quantum catalysis is a fascinating concept which demonstrates that certain transformations can only become possible when given access to a specific resource that has to be returned unaffected. It was first discovered in the context of entanglement theory and since then applied in a number of resource-theoretic frameworks, including quantum thermodynamics. Although in that case the necessary (and sometimes also sufficient) conditions on the existence of a catalyst are known, almost nothing is known about the precise form of the catalyst state required by the transformation. In particular, it is not clear whether it has to have some special properties or be finely tuned to the desired transformation. In this work we describe a surprising property of multi-copy states: we show that in resource theories governed by majorization all resourceful states are catalysts for all allowed transformations. In quantum thermodynamics this means that the so-called "second laws of thermodynamics" do not require a fine-tuned catalyst but rather any state, given sufficiently many copies, can serve as a useful catalyst. These analytic results are accompanied by several numerical investigations that indicate that neither a multi-copy form nor a very large dimension catalyst are required to activate most allowed transformations catalytically.

arXiv comment17 + 11 pages, 7 figures. Numerical results significantly extended. Comments welcome!

References in corpus (61)

• Concentrating Partial Entanglement by Local Operations
• Quantum Resource Theories
• Conditions for a class of entanglement transformations
• Quantum Thermodynamics
• The role of quantum information in thermodynamics --- a topical review
• Fundamental limitations for quantum and nano thermodynamics
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• 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
• General Entanglement Breaking Channels
• Robustness of entanglement
• Robustness of coherence: An operational and observable measure of quantum coherence
• Quantum coherence, time-translation symmetry and thermodynamics
• Application of a resource theory for magic states to fault-tolerant quantum computing
• The resource theory of informational nonequilibrium in thermodynamics
• The general structure of quantum resource theories
• Entanglement-assisted local manipulation of pure quantum states
• On-chip Maxwell's demon as an information-powered refrigerator
• The extraction of work from quantum coherence
• Experimental study of mutual information in a Maxwell Demon
• Robustness of asymmetry and coherence of quantum states
• (Quantumness in the context of) Resource Theories
• Quantum Reverse Shannon Theorem
• Conditions for coherence transformations under incoherent operations
• A derivation (and quantification) of the third law of thermodynamics
• An introductory review of the resource theory approach to thermodynamics
• The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
• Maximal Coherence and the Resource Theory of Purity
• Experimental rectification of entropy production by a Maxwell's Demon in a quantum system
• Embezzling Entangled Quantum States
• Operational one-to-one mapping between coherence and entanglement measures
• Experimental demonstration of information to energy conversion in a quantum system at the Landauer Limit
• Gibbs-Preserving Maps outperform Thermal Operations in the quantum regime
• Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality
• Catalytic Conversion Probabilities for Bipartite Pure States
• Necessary and Sufficient Conditions for the Trumping Relation
• Correlating thermal machines and the second law at the nanoscale
• Quantum message compression with applications
• All entangled states can demonstrate non-classical teleportation
• A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
• A measure of majorisation emerging from single-shot statistical mechanics
• Clock-work trade-off relation for coherence in quantum thermodynamics
• Limits to catalysis in quantum thermodynamics
• The trumping relation and the structure of the bipartite entangled states
• Coherence and asymmetry cannot be broadcast
• Relative submajorization and its use in quantum resource theories
• A sufficient set of experimentally implementable thermal operations
• Axiomatic approach to contextuality and nonlocality
• Avoiding irreversibility: engineering resonant conversions of quantum resources
• Necessary conditions on entanglement catalysts
• Finite-bath corrections to the second law of thermodynamics
• Approximate Majorization
• Thermodynamics of Minimal Coupling Quantum Heat Engines
• Estimating entanglement in teleportation experiments
• Characteristics of Universal Embezzling Families
• Moderate deviation analysis of majorisation-based resource interconversion
• Resource theory of quantum thermodynamics: Thermal operations and Second Laws
• Trade-off between multiple-copy transformation and entanglement catalysis
• Relation Between Catalyst-assisted Entanglement Transformation and Multiple-copy Transformation
• Asymptotic majorization of finite probability distributions

Cited by in corpus (27)

• Catalytic Transformations of Pure Entangled States
• Catalysis of entanglement and other quantum resources
• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• Fundamental Limits on Correlated Catalytic State Transformations
• Operational definition of the temperature of a quantum state
• Continuous thermomajorization and a complete set of laws for Markovian thermal processes
• Optimizing thermalizations
• Fundamental limits on anomalous energy flows in correlated quantum systems
• Catalytic leverage of correlations and mitigation of dissipation in Information erasure
• Catalytic Transformations in Coherence Theory
• Catalysis in Action via Elementary Thermal Operations
• Entanglement catalysis for quantum states and noisy channels
• Thermodynamically free quantum measurements
• Catalytic Gaussian thermal operations
• Quantum catalysis in cavity quantum electrodynamics
• Complete Characterization of Entanglement Embezzlement
• Catalytic transformations for thermal operations
• Quantum dichotomies and coherent thermodynamics beyond first-order asymptotics
• Communication with Quantum Catalysts
• Catalytic transformations with finite-size environments: applications to cooling and thermometry
• Role of energy-invariant assistants in energy extraction from quantum batteries
• Cooling and work extraction under memory-assisted Markovian thermal processes
• Minimizing Dissipation via Interacting Environments: Quadratic Convergence to Landauer Bound
• Unlocking inaccessible performance of the quantum refrigerator with catalysts
• Statistics of Entanglement Transformation with Hierarchies among Catalysts
• Finite-size catalysis in quantum resource theories
• Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group