General upper bounds for distributing conferencing keys in arbitrary quantum networks

Secure quantum conferencing refers to a protocol where a number of trusted users generate exactly the same secret key to confidentially broadcast private messages. By a modification of the techniques first introduced in [Pirandola, arXiv:1601.00966], we derive a single-letter upper bound for the maximal rates of secure conferencing in a quantum network with arbitrary topology, where the users are allowed to perform the most powerful local operations assisted by two-way classical communications, and the quantum systems are routed according to the most efficient multipath flooding strategies. More precisely, our analysis allows us to bound the ultimate rates that are achievable by single-message multiple-multicast protocols, where N senders distribute N independent secret keys, and each key is to be shared with an ensemble of M receivers.