Quantum Representation Learning Beyond Pairwise Fidelity

Quantum Physics arXiv:2609.01797 (quant-ph) [Submitted on 1 Sep 2026] Title:Quantum Representation Learning Beyond Pairwise Fidelity Authors:Junpeng Hou, Changbin Lu View a PDF of the paper titled Quantum Representation Learning Beyond Pairwise Fidelity, by Junpeng Hou and Changbin Lu View PDF HTML (experimental) Abstract:Quantum contrastive, metric, and self-supervised learning often expose encoded quantum states to the learner through transition probabilities, especially fidelity. Quantum states are known to possess higher-order relational invariants, but their consequences for learned representations remain unclear. Here we show that a transition-probability-only learning interface can possess exact continuous blind directions in certain quantum-state families. We recover this missing information with a batch operator, built from coherent overlap amplitudes and negative masking, where its second moment $q_-$ retains four-state interference. Moreover, $q_-$ is directly measurable through two-copy interference and can enter variational learning via methods like parameter shift. In relational quartets derived from toric-code and double-semion states, this fidelity-blind signal encodes inequivalent modular data despite identical pairwise fidelities. Finally, in a four-photon benchmark with preparation drift, augmenting all six pairwise fidelities at two orthogonal probes with the corresponding normalized $q_-$ reduces the mean out-of-distribution phase error by $86\%$ at equal total shot budget. These results establish multistate relational observables as measurable, trainable, and physically consequential signals for quantum representation learning beyond pairwise fidelity. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.01797 [quant-ph] (or arXiv:2609.01797v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.01797 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Junpeng Hou [view email] [v1] Tue, 1 Sep 2026 19:07:37 UTC (309 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Representation Learning Beyond Pairwise Fidelity, by Junpeng Hou and Changbin LuView 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?)