Full-state information-disturbance tradeoff for direction estimation with antiparallel spin-coherent pairs

[2606.18040] Full-state information-disturbance tradeoff for direction estimation with antiparallel spin-coherent pairs Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2606.18040 (quant-ph) [Submitted on 16 Jun 2026 ( v1 ), last revised 24 Aug 2026 (this version, v2)] Title: Full-state information-disturbance tradeoff for direction estimation with antiparallel spin-coherent pairs Authors: Massimiliano F. Sacchi View PDF HTML (experimental) Abstract: We determine the optimal information--disturbance tradeoff for estimating an unknown spatial direction encoded in two antiparallel spins. Rotational covariance reduces the optimization over all instruments to a finite-dimensional Choi problem: a positive seed operator obeys one trace constraint for each irreducible sector of the input representation, while both the directional score and the operation fidelity are linear functionals of this seed. For two antiparallel spin-$1/2$ particles, whose physical representation decomposes as $0\oplus1$, we derive the two-multiplier dual problem and characterize the optimal instrument from the kernel vectors of the dual slack operator. The optimal operation is a covariant filter with scalar--vector coherence and is generally not a convex interpolation between the identity channel and a measure-and-reprepare strategy. At maximum information we recover the Gisin--Popescu score, but the least disturbing output state is optimized independently, giving a smaller disturbance than both the parallel-spin benchmark and antiparallel measure-and-reprepare. We also formulate the parallel benchmark and, as a central extension of the method, treat antiparallel spin-coherent states of arbitrary spin $j$. In this case the signal coherently occupies all sectors $\ell=0,\ldots,2j$ of $j\otimes j$, the endpoint information is governed by nearest-neighbor sector coherences, and the endpoint disturbance is obtained from an explicit finite block-diagonal eigenvalue problem. Comments: Accepted version; 27 pages, 5 figures, 1 table Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.18040 [quant-ph] (or arXiv:2606.18040v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.18040 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. A 114, 022466 (2026) Related DOI : https://doi.org/10.1103/bgxx-s3qj Focus to learn more DOI(s) linking to related resources Submission history From: Massimiliano Federico Sacchi [ view email ] [v1] Tue, 16 Jun 2026 15:17:37 UTC (66 KB) [v2] Mon, 24 Aug 2026 09:50:43 UTC (68 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-06 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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