(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
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.