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Theory of direct measurement of the quantum pseudo-distribution via its characteristic function

arXiv Quantum Physics
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Researchers from the University of Toronto and the University of Rochester propose a novel method to directly measure quantum pseudo-distributions using characteristic functions, bypassing traditional reconstruction techniques. The approach leverages weak measurements of momentum translations to extract pseudo-distributions without prior theoretical assumptions, though quantum mechanics predicts alignment with the Kirkwood-Dirac distribution. Vandermonde matrices of eigenvalues are central to the theory, enabling data-driven extraction of joint and conditional pseudo-distributions linked to weak-value physics. By alternating position and momentum measurements, the team demonstrates direct verification of canonical commutation relations for any quantum state, offering experimental validation of fundamental quantum principles. This work establishes a constructive framework for measuring pseudo-distributions via characteristic functions, bridging theory and experiment in quantum metrology.
Theory of direct measurement of the quantum pseudo-distribution via its characteristic function

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Quantum Physics arXiv:2602.06145 (quant-ph) [Submitted on 5 Feb 2026] Title:Theory of direct measurement of the quantum pseudo-distribution via its characteristic function Authors:Andrew N. Jordan, David R. M. Arvidsson-Shukur, Aephraim M. Steinberg View a PDF of the paper titled Theory of direct measurement of the quantum pseudo-distribution via its characteristic function, by Andrew N. Jordan and 2 other authors View PDF HTML (experimental) Abstract:We propose a method for directly measuring the quantum mechanical pseudo-distribution of observable properties via its characteristic function. Vandermonde matrices of the eigenvalues play a central role in the theory. This proposal directly finds the pseudo-distribution using weak measurements of the generator of position moments (momentum translations). While the pseudo-distribution can be extracted from the data in a theory-agnostic way, it is shown that under quantum-mechanical formalism, the predicted pseudo-distribution is identified with the Kirkwood-Dirac pseudo-distribution. We discuss the construction of both the joint pseudo-distribution and a conditional pseudo-distribution, which is closely connected to weak-value physics. By permuting position and momentum measurements, we give a prescription to directly probe the canonical commutation relation and verify it for any quantum state. This work establishes the theory of a characteristic function approach to pseudo-distributions, as well as providing a constructive approach to measuring them directly. Comments: Subjects: Quantum Physics (quant-ph); Optics (physics.optics) Cite as: arXiv:2602.06145 [quant-ph] (or arXiv:2602.06145v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.06145 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Andrew N. Jordan [view email] [v1] Thu, 5 Feb 2026 19:32:00 UTC (160 KB) Full-text links: Access Paper: View a PDF of the paper titled Theory of direct measurement of the quantum pseudo-distribution via its characteristic function, by Andrew N. Jordan and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: physics physics.optics 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)

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Source: arXiv Quantum Physics