Strong superadditivity of the entanglement of formation follows from its additivity

Abstract

The additivity of both the entanglement of formation and the classical channel capacity is known to be a consequence of the strong superadditivity conjecture. We show that, conversely, the strong superadditivity conjecture follows from the additivity of the entanglement of formation; this means that the two conjectures are equivalent and that the additivity of the classical channel capacity is a consequence of them.

arXiv commentrevtex, 7 pages, research at Quantware MIPS Center http://www.quantware.ups-tlse.fr

References in corpus (7)

• Mixed State Entanglement and Quantum Error Correction
• Entanglement Measures under Symmetry
• The asymptotic entanglement cost of preparing a quantum state
• Variational Characterisations of Separability and Entanglement of Formation
• Additivity of the Classical Capacity of Entanglement-Breaking Quantum Channels
• Entanglement cost of mixed states
• On the Additivity of Entanglement of Formation

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