Magic Secret Sharing: Threshold Control of Quantum Computational Power via GHZ Entanglement
Summarize this article with:
Quantum Physics arXiv:2605.16614 (quant-ph) [Submitted on 15 May 2026] Title:Magic Secret Sharing: Threshold Control of Quantum Computational Power via GHZ Entanglement Authors:Soumyojyoti Dutta, Tushar View a PDF of the paper titled Magic Secret Sharing: Threshold Control of Quantum Computational Power via GHZ Entanglement, by Soumyojyoti Dutta and 1 other authors View PDF HTML (experimental) Abstract:We introduce Magic Secret Sharing (MSS), a quantum cryptographic primitive in which the secret is the computational capability of a quantum state rather than its classical description. In the resource theory of magic, non-stabilizer states fuel universal quantum computation via non-Clifford gates; MSS distributes this resource with an (n-1,n) threshold structure using a pre-shared GHZ state and a single local phase gate P(phi) = diag(1, exp(i*phi)). Any individual party holds the maximally mixed state I/2, with Wigner distance C(I/2) = 0, so no local operation can yield non-Clifford computational advantage regardless of what operations are applied or what noise acts on the device. The authorised coalition reconstructs magic content C(phi) = (|sin(phi)| + |cos(phi)| - 1)/2 exactly, enabling a logical T gate via gate teleportation in multi-server blind quantum computation (BQC). Among diagonal parametric gates, phase gates are the unique class satisfying the security condition, characterised via an exact column-sum condition. The protocol is elevated to a one-sided device-independent (1SDI) setting via a steering inequality: the assemblage produced on the recipient's side certifies magic delivery without trusting the coalition's devices. We demonstrate the (2,3) instance on ibm_marrakesh (156-qubit IBM Heron): security (C(rho_Bob) = 0.000, below LP reconstruction tolerance) holds in all runs, and state fidelity reaches 0.959-0.986 for the authorised party, with faithfulness confirmed for all four test values of phi including near-exact recovery (C = 0.154 vs theory 0.153) for phi = pi/8. Comments: Subjects: Quantum Physics (quant-ph) MSC classes: 81P45, 81P94, 81P68 Cite as: arXiv:2605.16614 [quant-ph] (or arXiv:2605.16614v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.16614 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Soumyojyoti Dutta [view email] [v1] Fri, 15 May 2026 20:33:49 UTC (126 KB) Full-text links: Access Paper: View a PDF of the paper titled Magic Secret Sharing: Threshold Control of Quantum Computational Power via GHZ Entanglement, by Soumyojyoti Dutta and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 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?)