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On Strong Superadditivity of the Entanglement of Formation

Koenraad M. R. Audenaert·Samuel L. Braunstein
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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 $E(ρ)=S(\trace_Aρ)$. We then consider the conjectured strong superadditivity of the entanglement of formation $E_F(ρ) \ge E_F(ρ_I)+E_F(ρ_{II})$, where $ρ_I$ and $ρ_{II}$ are the reductions of $ρ$ 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.

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Koenraad M. R. Audenaert, Samuel L. Braunstein. 2003-06-20. On Strong Superadditivity of the Entanglement of Formation. https://doi.org/10.1007/s00220-003-0987-1

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