Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy

TL;DR

This paper establishes sharp lower bounds for entanglement measures like entanglement of formation and squashed entanglement using an extended form of strong subadditivity of entropy, with explicit state constructions.

Contribution

It introduces new bounds for bipartite entanglement measures based on conditional entropy and constructs states that saturate these bounds, extending strong subadditivity principles.

Findings

Derived lower bounds for entanglement measures.

Constructed states that achieve the bounds.

Extended strong subadditivity of entropy.

Abstract

We prove lower bounds for the entanglement of formation and the squashed entanglement for any a bipartite density matrix in terms of the conditional entropy of the bipartite state with respect to either of its partial traces, and prove that these bounds are sharp by constructing a new class of states whose entanglements can be computed, and for which the bounds are saturated.