On strong superadditivity of the entanglement of formation
Audenaert, K.M.R.
and
Braunstein, S.L.

(2004):
*Communications in Mathematical Physics*
**246**,
443-452.
(PDF)
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*(Tr_{A}ρ). We then
consider the conjectured strong superadditivity of the entanglement of
formation
*E*_{F}(ρ)≥*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*^{*}. 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.