On the Cryptographic Structure Required for Verifying Qubits
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Quantum Physics arXiv:2606.05527 (quant-ph) [Submitted on 4 Jun 2026] Title:On the Cryptographic Structure Required for Verifying Qubits Authors:James Bartusek, Itay Shalit View a PDF of the paper titled On the Cryptographic Structure Required for Verifying Qubits, by James Bartusek and 1 other authors View PDF Abstract:Classically testing for the presence of anti-commuting operators on a quantum device is a critical tool underpinning recent progress in classical verification of quantum computation. While such tests can be based on cryptographic assumptions, known constructions rely on highly structured assumptions, e.g. trapdoor claw-free functions. In this work, we seek to explain this state of affairs by constructing strong cryptography from (certain forms of) classical tests of anti-commutation. In particular, we formulate the notion of a test of non-commutation (ToNC), an interactive protocol between a quantum prover and classical verifier in which the prover's final-round response is obtained by measuring one of two binary observables $P_0,P_1$ depending on the verifier's challenge bit $c$. We prove that, for a broad range of parameters, ToNC implies classical-communication key agreement (KA), and ToNC combined with one-way functions implies oblivious transfer (OT). Along the way, we develop tools for and provide the first known results on hardness amplification for post-quantum KA and OT, where communication is classical but adversaries may be quantum. In particular, we prove the following results of independent interest. - Post-quantum hard-core measure theorem: For any efficiently sampleable high-min-entropy distribution $D$ over pairs $(x,b)$ such that quantum circuits have advantage at most $\delta$ in predicting $b$ from $x$, there exists a sub-distribution $M\preceq D$ of density $(1-\delta)$ on which $b$ is nearly optimally quantum-hard to predict. - Post-quantum interactive XOR lemma: Given any classically-interactive protocol, if quantum adversaries have advantage at most $\delta$ in guessing a private challenger bit $b$, then two sequential repetitions reduce the advantage for predicting the XOR of the challenger bits $b_1\oplus b_2$ to at most $\delta^2+\rm{negl}(\lambda)$. Subjects: Quantum Physics (quant-ph); Cryptography and Security (cs.CR) Cite as: arXiv:2606.05527 [quant-ph] (or arXiv:2606.05527v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.05527 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Itay Shalit [view email] [v1] Thu, 4 Jun 2026 00:16:07 UTC (102 KB) Full-text links: Access Paper: View a PDF of the paper titled On the Cryptographic Structure Required for Verifying Qubits, by James Bartusek and 1 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?) 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?)