Optimizing Entanglement Manipulation via Algebraic-Geometric Decompositions and Semidefinite Programming Hierarchies

[2501.17394] Optimizing Entanglement Manipulation via Algebraic-Geometric Decompositions and Semidefinite Programming Hierarchies Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2501.17394 (quant-ph) [Submitted on 29 Jan 2025 ( v1 ), last revised 28 Aug 2026 (this version, v4)] Title: Optimizing Entanglement Manipulation via Algebraic-Geometric Decompositions and Semidefinite Programming Hierarchies Authors: Seiseki Akibue , Jisho Miyazaki , Hiroyuki Osaka View PDF HTML (experimental) Abstract: In the study of distributed quantum information processing, it is a fundamental problem to optimize local operations in the implementation of non-local quantum operations assisted by limited entanglement. We develop an algebraic-geometric framework that systematically simplifies optimization over separable (SEP) channels -- widely used as approximations of local operations -- and strengthens the Doherty--Parrilo--Spedalieri (DPS) hierarchy for solving such problems. We apply this framework to computing maximum success probability for exactly implementing a broad range of different non-local operations under SEP channels. First, we present a unified generalization of previous analytical results on the entanglement cost. Via the generalization, we resolve an open problem posed by Yu et al. regarding the entanglement cost of local state discrimination. Second, we numerically determine the trade-off between the strength of entanglement and the success probability of implementing various operations -- such as entanglement distillation, non-local unitary channels, measurements, and state verification. Comments: 51 pages, 7 figures Subjects: Quantum Physics (quant-ph) ; Mathematical Physics (math-ph) Cite as: arXiv:2501.17394 [quant-ph] (or arXiv:2501.17394v4 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2501.17394 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Lett Math Phys 116, 110 (2026) Related DOI : https://doi.org/10.1007/s11005-026-02138-9 Focus to learn more DOI(s) linking to related resources Submission history From: Seiseki Akibue [ view email ] [v1] Wed, 29 Jan 2025 03:16:30 UTC (5,456 KB) [v2] Wed, 1 Oct 2025 05:02:38 UTC (5,969 KB) [v3] Fri, 19 Jun 2026 22:15:05 UTC (5,550 KB) [v4] Fri, 28 Aug 2026 09:23:17 UTC (5,550 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2025-01 Change to browse by: math math-ph math.MP References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation 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? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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