aiqbench analysis
This paper introduces a novel chain rule for channel conditional entropies that enables fully adaptive security proofs for quantum key distribution protocols with no repetition rate limitations. By generalizing the entropy accumulation theorem under specific marginal-state constraints, the work advances fundamental techniques for analyzing prepare-and-measure QKD schemes in cryptographic applications.
Marginal-constrained entropy accumulation theorem
arXiv:2502.02563v5 Announce Type: replace Abstract: We derive a novel chain rule for a family of channel conditional entropies, covering von Neumann and sandwiched R\'{e}nyi entropies. In the process, we show that these channel conditional entropies are equal to their regularized version, and more generally, additive across tensor products of channels. For the purposes of cryptography, applying our chain rule to sequences of channels yields a new variant of R\'{e}nyi entropy accumulation, in which we can impose some specific forms of marginal-state constraint on the input states to each individual channel. This generalizes a recently introduced security proof technique that was developed to analyze prepare-and-measure QKD with no limitations on the repetition rate. In particular, our generalization yields ``fully adaptive'' protocols that can in principle update the entropy estimation procedure during the protocol itself, similar to the quantum probability estimation framework.
Abstract:We derive a novel chain rule for a family of channel conditional entropies, covering von Neumann and sandwiched Rényi entropies. In the process, we show that these channel conditional entropies are equal to their regularized version, and more generally, additive across tensor products of channels. For the purposes of cryptography, applying our chain rule to sequences of channels yields a new variant of Rényi entropy accumulation, in which we can impose some specific forms of marginal-state constraint on the input states to each individual channel. This generalizes a recently introduced security proof technique that was developed to analyze prepare-and-measure QKD with no limitations on the repetition rate. In particular, our generalization yields ``fully adaptive'' protocols that can in principle update the entropy estimation procedure during the protocol itself, similar to the quantum probability estimation framework.
See also the independent work [arXiv:2502.01611]. v5 changelog: Final version for publication in Quantum. Clarified the comparison with GEAT and added a figure illustrating the MEAT channel structure
arXiv:2502.02563 [quant-ph]
(or arXiv:2502.02563v5 [quant-ph] for this version)
Full text under the publisher's open licence · 171 words