Tight continuity bounds for quantum conditional mutual information

Establish tight continuity bounds for the quantum conditional mutual information I(A:B|C) for general tripartite quantum states ρ_ABC and σ_ABC in terms of their trace distance, improving upon existing Alicki–Fannes–Winter-type bounds.

Background

Quantum conditional mutual information (QCMI) is a central quantity in quantum information theory and underlies measures like the squashed entanglement and various channel capacities. Existing continuity bounds for QCMI (e.g., Alicki–Fannes–Winter) are not known to be tight.

The authors’ semi-continuity method yields tight continuity bounds for conditional entropy in certain cases, but does not directly provide tight bounds for QCMI. They explicitly leave the problem of deriving tight QCMI continuity bounds open.