One Key Good, L Keys Better: List Decoding Meets Quantum Privacy Amplification
Summarize this article with:
Quantum Physics arXiv:2603.18097 (quant-ph) [Submitted on 18 Mar 2026] Title:One Key Good, L Keys Better: List Decoding Meets Quantum Privacy Amplification Authors:Prateek P. Kulkarni View a PDF of the paper titled One Key Good, L Keys Better: List Decoding Meets Quantum Privacy Amplification, by Prateek P. Kulkarni View PDF HTML (experimental) Abstract:We introduce list privacy amplification (LPA), a relaxation of the final step of quantum key distribution (QKD) in which Alice and Bob extract a list of $L$ candidate keys from a raw string correlated with an eavesdropper Eve, with the guarantee that at least one key is perfectly secret while Eve cannot identify which. This parallels list decoding in error-correcting codes: relaxing unique decoding to list decoding increases the decoding radius; analogously, list extraction increases achievable key length beyond the standard quantum leftover hash lemma (QLHL). Within the abstract cryptography framework, we formalise LPA and prove the \emph{Quantum List Leftover Hash Lemma} (QLLHL): an $L$-list of $\ell$-bit keys can be extracted from an $n$-bit source with smooth min-entropy $k$ iff \[ \ell \le k + \log L - 2\log(1/\epsilon) - 3, \] yielding a tight additive $\log L$ gain over QLHL. This gain arises because the index of the secure key is chosen after hashing and hidden from Eve, effectively contributing $\log L$ bits of entropy. Applying QLLHL to BB84-type QKD, a list size $L = 2^{\alpha n'}$ increases the tolerable phase-error threshold from $h^{-1}(1 - h(e_b))$ to $h^{-1}(1 - h(e_b) + \alpha)$, exceeding the standard $\approx 11\%$ bound for any $\alpha > 0$. We prove tightness via a matching intercept-resend attack, establish composability with Wegman--Carter authentication, and present two constructions: a polynomial inner-product hash over $\mathbb{F}_{2^m}$ and a Toeplitz-based variant, running in $O(nL)$ and $O(nL \log n)$ time. Comments: Subjects: Quantum Physics (quant-ph); Cryptography and Security (cs.CR) Cite as: arXiv:2603.18097 [quant-ph] (or arXiv:2603.18097v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.18097 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Prateek P. Kulkarni [view email] [v1] Wed, 18 Mar 2026 10:37:05 UTC (19 KB) Full-text links: Access Paper: View a PDF of the paper titled One Key Good, L Keys Better: List Decoding Meets Quantum Privacy Amplification, by Prateek P. KulkarniView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: cs cs.CR References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)