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On strong superadditivity of the entanglement of formation

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JournalCommunications in Mathematical Physics
DatePublished - 1 Apr 2004
Issue number3
Volume246
Number of pages10
Pages (from-to)443-452
Original languageEnglish

Abstract

We employ a basic formalism from convex analysis to show a simple relation between the entanglement of formation E-F and the conjugate function E-* of the entanglement function E(rho)=S(Tr(A)rho). We then consider the conjectured strong superadditivity of the entanglement of formation E-F(rho)greater than or equal toE(F)(rho(I))+E-F(rho(II)), where rho(I) and rho(II) are the reductions of rho 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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