Necessary conditions on entanglement catalysts

Abstract

Given a pure state transformation $\psi \mapsto \varphi$ restricted to entanglement-assisted local operations with classical communication, we determine a lower bound for the dimension of a catalyst allowing that transformation. Our bound is stated in terms of the generalised concurrence monotones (the usual concurrence of two qubits is one such monotone). We further provide tools for deriving further conditions upon catalysts of pure state transformations.

Brief Report, 4 pages, accepted in PRA

References in corpus (3)

• Necessary and Sufficient Conditions for the Trumping Relation
• Catalytic Conversion Probabilities for Bipartite Pure States
• Inequalities that Collectively Completely Characterize the Catalytic Majorization Relation

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• Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
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• Catalytic Transformations of Pure Entangled States
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• All states are universal catalysts in quantum thermodynamics
• Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages
• Local convertibility of the ground state of the perturbed Toric code
• Non universality of entanglement convertibility
• The resource theory of nonclassicality of channel assemblages
• Entanglement-assisted local operations and classical communications conversion in the quantum critical systems
• Entanglement catalysis for quantum states and noisy channels
• Local Transformations of Multiple Multipartite States
• Bounds On Entanglement Catalysts
• Catalytic transformations for thermal operations
• Necessary conditions on effective quantum entanglement catalysts
• Catalytic transformations with finite-size environments: applications to cooling and thermometry
• A generalized dominance ordering for 1/2-BPS states
• Unlocking inaccessible performance of the quantum refrigerator with catalysts
• A finite sufficient set of conditions for catalytic majorization
• Statistics of Entanglement Transformation with Hierarchies among Catalysts
• Nontraditional Deterministic Remote State Preparation Using a Non-Maximally Entangled Channel without Additional Quantum Resources
• Advantage of flexible catalysis for entanglement and quantum thermodynamics