On the strong superadditivity of entanglement of formation -- Conditions and examples

TL;DR

This paper investigates the conditions under which the entanglement of formation exhibits strong superadditivity, identifying specific classes of quantum states where this property holds, thus clarifying longstanding questions in quantum information theory.

Contribution

It provides new conditions for strong superadditivity of entanglement of formation and identifies classes of states that satisfy these conditions.

Findings

Conditions for strong superadditivity established

Classes of states with strong superadditivity identified

Counterexamples from prior studies discussed

Abstract

From Shor's [Comm. Math. Phys. 246(3), 453 (2004)] and Hastings's [Nature Phys. 5, 255 (2009)] studies, the strong superadditivity of entanglement of formation is, in general, not true. In this paper, we provide conditions for strong superadditivity of entanglement of formation, and consequently identify classes of states that are strongly superadditive.