On Strong Superadditivity of the Entanglement of Formation |
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Authors: | Email author" target="_blank">Koenraad MR?AudenaertEmail author Samuel L?Braunstein |
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Institution: | (1) University of Wales, Bangor School of Informatics, Bangor (Gwynedd) LL57 1UT, UK;(2) The University of York, Dept. of Computer Science, York YO10 5DD, UK |
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Abstract: | We employ a basic formalism from convex analysis to show a simple relation between the entanglement of formation EF and the conjugate function E* of the entanglement function E()=S(TrA). We then consider the conjectured strong superadditivity of the entanglement of formation EF()EF(I)+EF(II), where I and II are the reductions of to the different Hilbert space copies, and prove that it is equivalent with subadditivity of E*. Furthermore, we show that strong superadditivity would follow from multiplicativity of the maximal channel output purity for quantum filtering operations, when purity is measured by Schatten p-norms for p tending to 1. |
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