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.

5+17 pages, 8 figures; published version

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• 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
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• Conditional quantum thermometry -- enhancing precision by measuring less
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• 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