Commutator Geometry and Information Preservation in the Quantum Switch

Quantum Physics arXiv:2609.21310 (quant-ph) [Submitted on 18 Sep 2026] Title:Commutator Geometry and Information Preservation in the Quantum Switch Authors:Xu Chen, Xue Ma View a PDF of the paper titled Commutator Geometry and Information Preservation in the Quantum Switch, by Xu Chen and Xue Ma View PDF HTML (experimental) Abstract:Two commuting channels yield the same composite channel in either fixed order, yet their quantum switch can alter information preservation. We study how this effect depends on the input state, retaining the joint output of the control and target. Exact Kraus commutator identities determine overlap and squared fidelity gaps. Fixed order preserves product inputs at least as well as the switch in fidelity. The reverse inequality holds for pure states of two qubits whose control Schmidt basis can be chosen to coincide with the order basis. A commutator matrix determines the target basis that maximizes the squared fidelity gap at fixed entanglement within this aligned family. For Pauli $X$ and $Y$ channels with equal error probabilities, the switch replaces a logical phase flip with an operator that stabilizes a joint code. At fixed noise, the switch preserves at least as much distinguishability and quantum Fisher information as fixed order for every state family in this code. For the pure encoded family studied here, exact formulas connect the phase information gain to the squared fidelity gap and quantify the reduction in information about the noise probability. Optimizing the probes yields equal maximal quantum Fisher information for noise estimation under both joint channels. These results connect commutator geometry and logical error structure to state preservation and the retention of encoded information. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.21310 [quant-ph] (or arXiv:2609.21310v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.21310 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Xu Chen [view email] [v1] Fri, 18 Sep 2026 04:36:25 UTC (327 KB) Full-text links: Access Paper: View a PDF of the paper titled Commutator Geometry and Information Preservation in the Quantum Switch, by Xu Chen and Xue MaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?)