This paper is concerned with an important theorem due to Fyodor L. Zak, which appeared in [Za1]: Let X ⊂ P be a (reduced and irreducible) subvariety. A k – secant space to X is a k – dimensional linear subspace of P which is spanned by k+1 points from X, the k – secant variety of X in P is the (closure of the) union of all the k – secant spaces of X. Zak denotes this space by S(X), we shall als...

It is known that the additivity conjecture of Holevo capacity, output minimum entoropy, and the entanglement of formation (EoF), are equivalent with each other. Among them, the output minimum entropy is simplest, and hence many researchers are focusing on this quantity. Here, we suggest yet another entanglement measure, whose strong superadditivity and additivity are equivalent to the additivit...

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(ρ) = S(TrAρ). We then consider the conjectured strong superadditivity of the entanglement of formation EF (ρ) ≥ EF (ρI ) + EF (ρII ), where ρI and ρII are the reductions of ρ to the different Hilbert space copies, and pr...

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(ρ) = S(TrA ρ). We then consider the conjectured strong superadditivity of the entanglement of formation EF (ρ) ≥ EF (ρI) + EF (ρII), where ρI and ρII are the reductions of ρ to the different Hilbert space copies, and prov...

Superadditivity relations characterize the distributions of coherence in multipartite quantum systems. In this work, we investigate superadditivity related to l1-norm $C_{l_{1}}$ multiqubit Tighter inequalities based on α-th ( $\alpha \geqslant 1$ ) power are presented for states under certain conditions, which include existing results as special cases. These give rise finer characterization am...

This paper investigates the superadditivity of the maximum achievable information rate in a quantum channel. The superadditivity is a phenomenon that the maximum accessible information per channel strictly increases as the number of quantum states jointly measured increases. We give an explanation of this phenomenon by comparing the quantum channel with the classical discrete memoryless channel...