Advantage of flexible catalysis for entanglement and quantum thermodynamics

Abstract

Understanding the fundamental limits of state convertibility is crucial for establishing the boundaries of quantum information processing and thermodynamic efficiency. While auxiliary systems, catalysts, can facilitate otherwise impossible transformations, standard catalysis rigidly requires the auxiliary system to return to its exact initial state. In this work, we investigate the power of flexible catalysis, where the catalyst evolves through a cycle of states, restoring its initial configuration only after a finite number of steps. Focusing on the regime of fixed, finite dimensions, we analyze the capabilities of flexible catalysis within the resource theories of entanglement and quantum thermodynamics. In the context of entanglement, we derive conditions limiting flexible catalysts, yet show that flexible catalysis can be strictly more powerful than same-dimensional standard catalysis: it enables deterministic transformations achievable by no standard catalyst of the same dimension, and it strictly increases the success probability of stochastic local operations and classical communication. A similar deterministic advantage arises in quantum thermodynamics, where flexible catalysis enables state transformations that are impossible with any standard catalyst of fixed dimension and Hamiltonian but become achievable via flexible catalysis.

arXiv comment5+6 pages, 2 figures, conjecture revised to theorem

References in corpus (29)

• Quantum entanglement
• Circuit Quantum Electrodynamics
• NMR Techniques for Quantum Control and Computation
• Conditions for a class of entanglement transformations
• Fundamental limitations for quantum and nano thermodynamics
• The second laws of quantum thermodynamics
• Quantum coherence, time-translation symmetry and thermodynamics
• Entanglement of pure states for a single copy
• Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
• Entanglement-assisted local manipulation of pure quantum states
• An introductory review of the resource theory approach to thermodynamics
• Embezzling Entangled Quantum States
• Gibbs-Preserving Maps outperform Thermal Operations in the quantum regime
• Correlating thermal machines and the second law at the nanoscale
• Von Neumann entropy from unitarity
• Limits to catalysis in quantum thermodynamics
• Catalytic quantum teleportation and beyond
• Quantum thermodynamics of correlated-catalytic state conversion at small-scale
• Relative submajorization and its use in quantum resource theories
• Catalysis of entanglement and other quantum resources
• Multiple-copy entanglement transformation and entanglement catalysis
• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• Fundamental Limits on Correlated Catalytic State Transformations
• Necessary conditions on entanglement catalysts
• Resources of the Quantum World
• Coherence manipulation in asymmetry and thermodynamics
• Bounds On Entanglement Catalysts
• Catalytic and asymptotic equivalence for quantum entanglement
• Catalytic transformations for thermal operations