Private-message quantum broadcast capacity regions

A broadcast channel maps one sender's input to two receiver systems. The achievable region depends on what each receiver must recover and which auxiliary resources are allowed. A “full classical–quantum–entanglement region” is not one defined task without those choices.

Yard–Hayden–Devetak and Savov–Wilde established coding results and achievable regions in specified degraded, classical–quantum and other settings. Quantum superposition and Marton-type coding give inner bounds; some structured channel families admit matching characterizations. These results should be recorded with their message and assistance hypotheses.

Preprint progress (August 2026, classical subproblem): Huang–Yanxiao Liu–Yi Liu claim an explicit two-receiver discrete memoryless classical broadcast channel for which Marton's inner bound is strictly suboptimal. Since classical channels embed in the unassisted classical-message task, this challenges a candidate general formula within that subproblem. It does not resolve a quantum broadcast region or block progress on quantum special cases.

The programme is to close well-defined inner/outer-bound gaps for named channel families, while keeping other communication tasks as separately labeled variants.

Source disclosures

Huang, Liu and Liu report GPT-5.6 Sol and Claude Fable/Opus assistance with numerical and analytic searches, and acknowledge human verification and editorial help. This is an author disclosure, not independent proof verification. Source

Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.

preprint: Marton's inner bound is claimed suboptimal for an explicit classical broadcast channel; this is a classical subproblem, not a quantum capacity-region theorem. Evidence