Tight continuity bounds for squashed entanglement

Establish tight continuity bounds for the squashed entanglement E_sq(ρ_AB) with respect to perturbations in the state (e.g., trace distance), improving upon the original Alicki–Fannes-type continuity bound.

Background

Squashed entanglement is an important entanglement measure with strong operational and structural properties. Known continuity bounds rely on Alicki–Fannes-type arguments and are not tight.

Improving the continuity of QCMI would directly impact the continuity of squashed entanglement, given its definition via conditional mutual information. The authors explicitly note this as a closely related open question.