Equivalence of non-local computation tasks beyond Clifford operations
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Quantum Physics arXiv:2606.26354 (quant-ph) [Submitted on 24 Jun 2026] Title:Equivalence of non-local computation tasks beyond Clifford operations Authors:Andreas Bluhm, Simon Höfer, Alex May, Florian Speelman, Philip Verduyn Lunel View a PDF of the paper titled Equivalence of non-local computation tasks beyond Clifford operations, by Andreas Bluhm and 4 other authors View PDF Abstract:Non-local quantum computation (NLQC) studies how two collaborating players can implement channels on distributed systems using a single simultaneous round of quantum communication and shared entanglement. NLQC has applications in diverse areas, ranging from quantum position-verification to quantum gravity. Recently, it has been realized that the relationships among families of NLQC tasks are highly structured: many seemingly distinct tasks are related by reductions, wherein implementations of one task can be used to efficiently implement a second task. This is analogous to the notion of reduction in complexity theory, and reveals the relative hardness of NLQC tasks. In this work we continue the study of reductions among NLQC tasks. We focus on NLQC examples of the greatest interest in quantum position-verification; in particular examples involving large classical inputs and fixed-size quantum inputs, since these constitute the most feasible protocols for position-verification schemes. Within this setting, we find many new relationships among NLQC tasks. For instance, protocols for the simplest example of redirecting a quantum system based on a classical control imply protocols for controlled single qubit measurements in arbitrary bases, the controlled application of any Clifford unitary, and even the controlled application of any unitary of the form $U=C_1DC_0$ with $D$ an arbitrary diagonal unitary and $C_0, C_1$ Clifford circuits. This implies that many feasible position-verification schemes have the same asymptotic scaling for their entanglement cost, and hence a similar level of security. Our techniques rely on ideas from gate teleportation and measurement based quantum computation, among other areas, bringing several new strategies into NLQC which may be of independent interest. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.26354 [quant-ph] (or arXiv:2606.26354v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.26354 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Alex May [view email] [v1] Wed, 24 Jun 2026 19:59:21 UTC (72 KB) Full-text links: Access Paper: View a PDF of the paper titled Equivalence of non-local computation tasks beyond Clifford operations, by Andreas Bluhm and 4 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)