Quantum Broadcast Channels with Mutually Confidential Messages
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.
Related
- Non-asymptotic Sphere-Packing Bounds for Finite-Blocklength Scalar Gaussian Multiple-Access and Broadcast Channels
- Rateless Nested Lattice Codes for Secure Cooperative V2X Broadcast over Fading and Erasure Channels
- Quantum channels on duals of von Neumann algebras in the Schrödinger picture
- Quantum-State Oblivious Transfer over Quantum Erasure Channels
- The exact strong converse exponent for private communication over quantum channels
BibTeX
@misc{belzig2026quantum,
title = {{Quantum Broadcast Channels with Mutually Confidential Messages}},
author = {Paula Belzig and Sukanya Ghosal and Farzin Salek and Graeme Smith},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26750},
eprint = {2609.26750},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26750},
}
RIS
TY - UNPB
TI - Quantum Broadcast Channels with Mutually Confidential Messages
AU - Paula Belzig
AU - Sukanya Ghosal
AU - Farzin Salek
AU - Graeme Smith
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26750
UR - https://arxiv.org/abs/2609.26750
AB - 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.
ER -