Quantum channels enable confidential messages for multiple users
Quantum Broadcast Channels with Mutually Confidential Messages
Information Theory
Summary
This paper studies how to send secret messages to two different people using quantum communication channels so that each person cannot learn the other's message, even if they already know their own. The authors develop mathematical methods to show when this kind of secret communication is possible and how large the message rates can be under these secrecy constraints. They also compare sending secret classical messages to sending quantum information, finding some differences in what rates are achievable. Their work applies to various types of quantum channels, including some that behave like well-known classical channels.
What this means in practice
- •For quantum communication engineers: Design secure quantum communication systems that send different secret classical messages to multiple receivers over quantum channels.
- •For quantum network designers: Determine achievable confidential communication rates when building quantum networks that handle multiple users with secrecy constraints.
Authors
Paula Belzig, Sukanya Ghosal, Farzin Salek, Graeme Smith
Abstract
We study the transmission of two independent confidential classical messages over a quantum broadcast channel, one for each receiver. Each message must remain secret from the other receiver, including when that receiver knows its own message. For classical inputs and quantum outputs, we establish the classical Marton-type inner bound under average reliability and conditional strong secrecy. The encoder selects pairs of codewords from independently generated codebooks using normalized likelihood weights. We prove reliability through a change-of-distribution argument. Our main technical result is a bipartite classical-quantum resolvability theorem that accounts for the dependence created by pair selection and establishes secrecy for the same encoder. We also obtain a multi-letter capacity characterization and extend it to arbitrary quantum inputs under secrecy against the other receiver, together with the Stinespring environment. We recover confidential capacity regions for deterministic classical and degraded classical-quantum channels, with an explicit evaluation for the classical Blackwell channel. For coherent isometric extensions of injective deterministic classical broadcast channels, we show that the confidential classical capacity region equals that of the corresponding classical channel. We then compare confidential classical communication with quantum transmission. For the coherent isometric extension of the Blackwell channel, we determine the unassisted quantum-capacity region and show that some achievable confidential classical rate pairs lie outside it. The Platypus channel provides another example of this separation.