Catalytic Transformations of Pure Entangled States

Abstract

Quantum entanglement of pure states is usually quantified via the entanglement entropy, the von Neumann entropy of the reduced state. Entanglement entropy is closely related to entanglement distillation, a process for converting quantum states into singlets, which can then be used for various quantum technological tasks. The relation between entanglement entropy and entanglement distillation has been known only for the asymptotic setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Here we close this gap by considering entanglement catalysis. We prove that entanglement entropy completely characterizes state transformations in the presence of entangled catalysts. Our results imply that entanglement entropy quantifies the amount of entanglement available in a bipartite pure state to be used for quantum information processing, giving asymptotic results an operational meaning also in the single-copy setup.

arXiv comment5+2 pages, 2 figures. Accepted for publication in Physical Review Letters

References in corpus (36)

• Quantum entanglement
• Concentrating Partial Entanglement by Local Operations
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Quantifying Entanglement
• Quantum Coherence as a Resource
• Conditions for a class of entanglement transformations
• The second laws of quantum thermodynamics
• Quantum information can be negative
• Catalytic Coherence
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• Necessary and Sufficient Conditions for the Trumping Relation
• Von Neumann entropy from unitarity
• Catalytic quantum teleportation and beyond
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• Coherence and asymmetry cannot be broadcast
• Catalytic coherence transformations
• Multiple-copy entanglement transformation and entanglement catalysis
• Catalysis of entanglement manipulation for mixed states
• Entropy and reversible catalysis
• Catalytic majorization and ${\ell }_p$ norms
• Inequalities that Collectively Completely Characterize the Catalytic Majorization Relation
• All states are universal catalysts in quantum thermodynamics
• Necessary conditions on entanglement catalysts
• Is coherence catalytic?
• Rates of multi-partite entanglement transformations and applications in quantum networks
• Bounds On Entanglement Catalysts
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Cited by in corpus (14)

• Catalysis of entanglement and other quantum resources
• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• Entropy and reversible catalysis
• Fundamental Limits on Correlated Catalytic State Transformations
• Is there a finite complete set of monotones in any quantum resource theory?
• Correlations in typicality and an affirmative solution to the exact catalytic entropy conjecture
• Catalytic leverage of correlations and mitigation of dissipation in Information erasure
• Catalytic Transformations in Coherence Theory
• Catalysis in Action via Elementary Thermal Operations
• Covariant catalysis requires correlations and good quantum reference frames degrade little
• Entanglement catalysis for quantum states and noisy channels
• Transcendental properties of entropy-constrained sets
• Delocalized and Dynamical Catalytic Randomness and Information Flow
• Statistics of Entanglement Transformation with Hierarchies among Catalysts