Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy

Abstract

We prove lower bounds for the entanglement of formation and the squashed entanglement for any a bipartite density matrix in terms of the conditional entropy of the bipartite state with respect to either of its partial traces, and prove that these bounds are sharp by constructing a new class of states whose entanglements can be computed, and for which the bounds are saturated.

8 pages. Version 2 includes some additional references and comments

References in corpus (5)

• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Faithful Squashed Entanglement
• Nonadditivity of quantum and classical capacities for entanglement breaking multiple-access channels and butterfly network
• On Conjectures of Classical and Quantum Correlations in Bipartite States
• Lower bounds on the squashed entanglement for multi-party systems

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• Extensive Long-Range Entanglement in a Nonequilibrium Steady State
• Computing partial traces and reduced density matrices
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• Distribution of Mutual Information in Multipartite States
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• A new operator extension of strong subadditivity of quantum entropy
• Entropic witness for quantum memory in open system dynamics
• Maximally entangling states and dynamics in one dimensional nearest neighbor Floquet systems
• Reexamination of strong subadditivity: A quantum-correlation approach
• The Saturation of Several Universal Inequalities in Information-Processing
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• Theory dependence of black hole interior reconstruction and the extended strong subadditivity
• Entanglement production in the decay of a metastable state
• Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors