Composable, unconditional security without a Quantum secret key: public broadcast channels and their conceptualizations, adaptive bit transmission rates, fidelity pruning under wiretaps

TL;DR

This paper explores the potential for achieving unconditional security in quantum communication over public broadcast channels without relying on secret keys, by analyzing channel properties, fidelity pruning, and Eve's error probabilities.

Contribution

It introduces methods to analyze and enhance security in quantum channels without secret keys, including fidelity pruning and cascading techniques to increase Eve's error probability.

Findings

Eve's error probability can be increased via cascading channels.

Holevo information analysis helps evaluate Eve's decoding success.

Post-processing reduces Holevo quantities, improving security.

Abstract

We examine public broadcast, forward conceptual, and backward conceptual, Quantum channels in the context of communication protocols that are independent of secret keys. Given research directions of interest previously identified in arXiv: 1804.01797, besides converse upper bounds on the bit transmission rate obtained by the author in recent work (arXiv: 2507.03035), additional possibilities remain, including: (1) determining whether aspects of QKD dependent protocols can be incorporated into steps of QKD independent protocols; (2) whether there would be any amplification to the Quantum-classical performance gap that Alice and Bob can exploit towards prospective Quantum advantage; (3) formulating the conditions under which secrecy and authentication can be simultaneously achieved. To characterize the conditions for which secrecy can be achieved with high probability, we argue that there not only exists suitable protocols which enable Alice and Bob to map into the authenticated space of bit codewords with high probability, but also that forward conceptual channels, through cascading, can significantly increase Eve's probability of false acceptance. Albeit the fact that secrecy, along with conceputalizations of the public broadcast channel, were initially discussed by Maurer for QKD dependent protocols, determining whether aspects of such protocols can be adapted for unconditional security without the use of a secret key is of great interest to explore. We demonstrate that Eve's error probability, through the cascading procedure, can be analyzed with the Holevo information under an optimal decoder. Furthermore, through post-processing of the outputs of a Completely Positive Trace Preserving (CPTP) map, we also demonstrate how to decrease Holevo sum quantities with data-processing and entropy-continuity bounds.