On Strong Superadditivity of the Entanglement of Formation
Audenaert, K M R, Braunstein, S L · CERN Document Server (European Organization for Nuclear Research) · 2003
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 $E(\\rho)=S(\\trace_A\\rho)$. We then consider the conjectured strong superadditivity of the entanglement of formation $E_F(\\rho) \\ge E_F(\\rho_I)+E_F(\\rho_{II})$, 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 $E^*$. As an application, we show that strong superadditivity would follow from multiplicativity of the maximal channel output purity for all non-trace-preserving quantum channels, when purity is measured by Schatten $p$-norms for $p$ tending to 1.