Key Assistance, Key Agreement, and Layered Secrecy for Bosonic Broadcast Channels

Secret-sharing building blocks based on quantum broadcast communication are studied. The confidential capacity region of the pure-loss bosonic broadcast channel is determined with key assistance, under the assumption of the long-standing minimum output-entropy conjecture. If the main receiver has a transmissivity of $\eta\lt\frac{1}{2}$, then confidentiality solely relies on the key-assisted encryption of the one-time pad. We also address conference key agreement for the distillation of two keys, a public key and a secret key. A regularized formula is derived for the key-agreement capacity region. In the pure-loss bosonic case, the key-agreement region is included within the capacity region of the corresponding broadcast channel with confidential messages. We then consider a network with layered secrecy, where three users with different security ranks communicate over the same broadcast network. We derive an achievable layered-secrecy region for a pure-loss bosonic channel that is formed by the concatenation of two beam splitters.