Classical capacity, quantum recovery, and secrecy

A density operator has distillable key, not a channel classical capacity, unless a state-to-channel interface is explicitly provided. Accordingly, the sentence “a zero-key state has positive classical capacity” is ill-typed without that interface. The correct separation is that a zero-key theorem for a state/protocol pair supplies no zero upper bound on an unrelated channel's Holevo information.

The Oai272-A conversation draft is retained only as a scoped secret-bit comparison Oai272Draft. It is not used to prove any entropy statement in this manuscript.