Multiple-copy entanglement transformation and entanglement catalysis

Abstract

We prove that any multiple-copy entanglement transformation [S. Bandyopadhyay, V. Roychowdhury, and U. Sen, Phys. Rev. A \textbf{65}, 052315 (2002)] can be implemented by a suitable entanglement-assisted local transformation [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. \textbf{83}, 3566 (1999)]. Furthermore, we show that the combination of multiple-copy entanglement transformation and the entanglement-assisted one is still equivalent to the pure entanglement-assisted one. The mathematical structure of multiple-copy entanglement transformations then is carefully investigated. Many interesting properties of multiple-copy entanglement transformations are presented, which exactly coincide with those satisfied by the entanglement-assisted ones. Most interestingly, we show that an arbitrarily large number of copies of state should be considered in multiple-copy entanglement transformations.

11 pages, RevTex 4. Main results unchanged. Journal version

References in corpus (6)

• Concentrating Partial Entanglement by Local Operations
• Conditions for a class of entanglement transformations
• Entanglement of pure states for a single copy
• Entanglement-assisted local manipulation of pure quantum states
• The trumping relation and the structure of the bipartite entangled states
• A classification of incomparable states

Cited by in corpus (37)

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• Catalytic Conversion Probabilities for Bipartite Pure States
• Necessary and Sufficient Conditions for the Trumping Relation
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• Quantum thermodynamics of correlated-catalytic state conversion at small-scale
• Resource convertibility and ordered commutative monoids
• Catalytic Transformations of Pure Entangled States
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• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• Catalytic majorization and ${\ell }_p$ norms
• Fundamental Limits on Correlated Catalytic State Transformations
• Majorization uncertainty relations for mixed quantum states
• Majorization relations and entanglement generation in a beam splitter
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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
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• Catalytic Transformations in Coherence Theory
• Entanglement-assisted transformation is asymptotically equivalent to multiple-copy transformation
• Two constructive proofs on d-majorization and thermo-majorization
• Relation Between Catalyst-assisted Entanglement Transformation and Multiple-copy Transformation
• Trade-off between multiple-copy transformation and entanglement catalysis
• Entanglement catalysis for quantum states and noisy channels
• Catalytic and asymptotic equivalence for quantum entanglement
• Matrix majorization in large samples
• Teleportation with Embezzling Catalysts
• Quantum thermodynamics with coherence: Covariant Gibbs-preserving operation is characterized by the free energy
• An Equivalence of Entanglement-Assisted Transformation and Multiple-Copy Entanglement Transformation
• Communication with Quantum Catalysts
• Matrix Majorization in Large Samples with Varying Support Restrictions
• Approximate and ensemble local entanglement transformations for multipartite states
• Catalytic Activation of Bell Nonlocality
• Finite-size catalysis in quantum resource theories
• Advantage of flexible catalysis for entanglement and quantum thermodynamics
• Partial Recovery of Quantum Entanglement
• Conditions for Large-Sample Majorization of Pairs of Flat States in Terms of $\alpha$-z Relative Entropies