Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence

Abstract

Quantum resource manipulation may include an ancillary state called a catalyst, which aids the transformation while restoring its original form at the end, and characterizing the enhancement enabled by catalysts is essential to reveal the ultimate manipulability of the precious resource quantity of interest. Here, we show that allowing correlation among multiple catalysts can offer arbitrary power in the manipulation of quantum coherence. We prove that any state transformation can be accomplished with an arbitrarily small error by covariant operations with catalysts that may create a correlation within them while keeping their marginal states intact. This presents a new type of embezzlement-like phenomenon, in which the resource embezzlement is attributed to the correlation generated among multiple catalysts. We extend our analysis to general resource theories and provide conditions for feasible transformations assisted by catalysts that involve correlation, putting a severe restriction on other quantum resources for showing this anomalous enhancement, as well as characterizing achievable transformations in relation to their asymptotic state transformations. Our results provide not only a general overview of the power of correlation in catalysts but also a step toward the complete characterization of the resource transformability in quantum thermodynamics with correlated catalysts.

arXiv comment5+17 pages, 8 figures; published version

References in corpus (76)

• Concentrating Partial Entanglement by Local Operations
• Quantifying Coherence
• Quantum metrology
• Quantum Resource Theories
• The Role of Relative Entropy in Quantum Information Theory
• Operational Resource Theory of Coherence
• Reference frames, superselection rules, and quantum information
• Fundamental limitations for quantum and nano thermodynamics
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• The second laws of quantum thermodynamics
• Catalytic Coherence
• Quantum coherence, time-translation symmetry and thermodynamics
• "Squashed Entanglement" - An Additive Entanglement Measure
• The resource theory of quantum reference frames: manipulations and monotones
• The resource theory of informational nonequilibrium in thermodynamics
• The general structure of quantum resource theories
• Entanglement-assisted local manipulation of pure quantum states
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• The extraction of work from quantum coherence
• (Quantumness in the context of) Resource Theories
• Continuity of quantum conditional information
• Optimal Cloning of Pure States, Judging Single Clones
• The theory of manipulations of pure state asymmetry: basic tools and equivalence classes of states under symmetric operations
• An introductory review of the resource theory approach to thermodynamics
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Superselection rules and quantum protocols
• Embezzling Entangled Quantum States
• Metric adjusted skew information
• Resource Destroying Maps
• Quantifying quantum resources with conic programming
• Operational Advantage of Quantum Resources in Subchannel Discrimination
• One-shot coherence distillation
• A Generalization of Quantum Stein's Lemma
• Necessary and Sufficient Conditions for the Trumping Relation
• Catalytic Conversion Probabilities for Bipartite Pure States
• One-Shot Operational Quantum Resource Theory
• No-Go Theorems for Quantum Resource Purification
• Convex geometry of quantum resource quantification
• Correlating thermal machines and the second law at the nanoscale
• Von Neumann entropy from unitarity
• One-Shot Coherence Dilution
• Conservative Quantum Computing
• Stochastic independence as a resource in small-scale thermodynamics
• Benchmarking one-shot distillation in general quantum resource theories
• Catalytic quantum teleportation and beyond
• Limits to catalysis in quantum thermodynamics
• Quantifying resource in catalytic resource theory
• Quantum thermodynamics of correlated-catalytic state conversion at small-scale
• Coherence and asymmetry cannot be broadcast
• Catalytic coherence transformations
• A no-broadcasting theorem for quantum asymmetry and coherence and a trade-off relation for approximate broadcasting
• Third Law of Thermodynamics as a Single Inequality
• Skew informations from an operational view via resource theory of asymmetry
• Catalytic Transformations of Pure Entangled States
• Detecting metrologically useful asymmetry and entanglement by a few local measurements
• Uncertainty relations in implementation of unitary operations
• Coherence distillation machines are impossible in quantum thermodynamics
• Multiple-copy entanglement transformation and entanglement catalysis
• Entropy and reversible catalysis
• Catalytic majorization and ${\ell }_p$ norms
• A generalization of majorization that characterizes Shannon entropy
• Fundamental energy requirement of reversible quantum operations
• Dephasing-Covariant Operations Enable Asymptotic Reversibility of Quantum Resources
• All states are universal catalysts in quantum thermodynamics
• The Wigner-Yanase entropy is not subadditive
• Catalytic quantum randomness
• General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures
• Coherence cost for violating conservation laws
• Universal limitations on implementing resourceful unitary evolutions
• Building all Time Evolutions with Rotationally Invariant Hamiltonians
• Amplifying asymmetry with correlated catalysts
• By-passing fluctuation theorems
• The variance of relative surprisal as single-shot quantifier
• General state transitions with exact resource morphisms: a unified resource-theoretic approach
• On the failure of subadditivity of the Wigner-Yanase entropy

Cited by in corpus (31)

• Catalytic quantum teleportation and beyond
• Catalysis of entanglement and other quantum resources
• Fundamental Limits on Correlated Catalytic State Transformations
• Is there a finite complete set of monotones in any quantum resource theory?
• Fundamental limits on anomalous energy flows in correlated quantum systems
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
• Catalytic Transformations in Coherence Theory
• Catalysis in Action via Elementary Thermal Operations
• Coherence manipulation in asymmetry and thermodynamics
• No-go theorem for entanglement distillation using catalysis
• Entanglement catalysis for quantum states and noisy channels
• Quantum catalysis in cavity quantum electrodynamics
• Complete Characterization of Entanglement Embezzlement
• A hierarchy of thermal processes collapses under catalysis
• Second Law of Entanglement Manipulation with Entanglement Battery
• Catalytic transformations for thermal operations
• Beyond i.i.d. in the Resource Theory of Asymmetry: An Information-Spectrum Approach for Quantum Fisher Information
• Black Box Work Extraction and Composite Hypothesis Testing
• Quantum thermodynamics with coherence: Covariant Gibbs-preserving operation is characterized by the free energy
• Coherence, superposition, and Löwdin symmetric orthogonalization
• Conditional quantum thermometry -- enhancing precision by measuring less
• Catalytic Activation of Bell Nonlocality
• Cooling and work extraction under memory-assisted Markovian thermal processes
• Censorship of quantum resources against catalytic account sharing
• Experimental Catalytic Amplification of Asymmetry
• Strong symmetries in collision models and physical dilations of covariant quantum maps
• Unspeakable Coherence Concentration
• Finite-size catalysis in quantum resource theories
• Advantage of flexible catalysis for entanglement and quantum thermodynamics
• Macroscopicity and observational deficit in states, operations, and correlations
• Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group