Fundamental Limits on Correlated Catalytic State Transformations

Abstract

Determining whether a given state can be transformed into a target state using free operations is one of the fundamental questions in the study of resources theories. Free operations in resource theories can be enhanced by allowing for a catalyst system that assists the transformation and is returned unchanged, but potentially correlated, with the target state. While this has been an active area of recent research, very little is known about the necessary properties of such catalysts. Here, we prove fundamental limits applicable to a large class of correlated catalytic transformations by showing that a small residual correlation between catalyst and target state implies that the catalyst needs to be highly resourceful. In fact, the resources required diverge in the limit of vanishing residual correlation. In addition, we establish that in imperfect catalysis a small error generally implies a highly resourceful embezzling catalyst. We develop our results in a general resource theory framework and discuss its implications for the resource theory of athermality, the resource theory of coherence and entanglement theory.

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Cited by in corpus (25)

• Catalysis of entanglement and other quantum resources
• Is there a finite complete set of monotones in any quantum resource theory?
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• Correlations in typicality and an affirmative solution to the exact catalytic entropy conjecture
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
• Fidelity-Based Smooth Min-Relative Entropy: Properties and Applications
• Catalysis in Action via Elementary Thermal Operations
• No-go theorem for entanglement distillation using catalysis
• Entanglement catalysis for quantum states and noisy channels
• Catalytic and asymptotic equivalence for quantum entanglement
• Quantum catalysis in cavity quantum electrodynamics
• Complete Characterization of Entanglement Embezzlement
• Catalytic transformations for thermal operations
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• Transcendental properties of entropy-constrained sets
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• Communication with Quantum Catalysts
• Quantum thermodynamics with coherence: Covariant Gibbs-preserving operation is characterized by the free energy
• Correlated dynamics as a resource in molecular switches
• Towards the ultimate limits of quantum channel discrimination and quantum communication
• Multipartite entanglement theory with entanglement-nonincreasing operations
• Physical consequences of Lindbladian invariance transformations
• Advantage of flexible catalysis for entanglement and quantum thermodynamics
• A fixed-point algorithm for matrix projections with applications in quantum information
• Finite-size catalysis in quantum resource theories