Quantum trajectories for time-binned data and their closeness to fully conditioned quantum trajectories

Quantum Physics arXiv:2601.10937 (quant-ph) [Submitted on 16 Jan 2026] Title:Quantum trajectories for time-binned data and their closeness to fully conditioned quantum trajectories Authors:Nattaphong Wonglakhon, Areeya Chantasri, Howard M. Wiseman View a PDF of the paper titled Quantum trajectories for time-binned data and their closeness to fully conditioned quantum trajectories, by Nattaphong Wonglakhon and Areeya Chantasri and Howard M. Wiseman View PDF Abstract:Quantum trajectories are dynamical equations for quantum states conditioned on the results of a time-continuous measurement, such as a continuous-in-time current $\vec y_t$. Recently there has been renewed interest in dynamical maps for quantum trajectories with time-intervals of finite size $\Delta t$. Guilmin \emph{et al.} (unpublished) derived such a dynamical map for the (experimentally relevant) case where only the average current $I_t$ over each interval is available. Surprisingly, this binned data still generates a conditioned state $\rho_\text{\faFaucet}$ that is almost pure (for efficient measurements), with an impurity scaling as $(\Delta t)^{3}$. We show that, nevertheless, the typical distance of $\rho_\text{\faFaucet}$ from $\hat{\psi}_{\text{F}; \vec y_t}$ -- the projector for the pure state conditioned on the full current -- is as large as $(\Delta t)^{3/2}$. We introduce another finite-interval dynamical map (``$\Phi$-map''), which requires only one additional real statistic, $\phi_t$, of the current in the interval, that gives a conditioned state $\hat{\psi}_\Phi$ which is only $(\Delta t)^{2}$-distant from $\hat{\psi}_{\text{F}; \vec y_t}$. We numerically verify these scalings of the error (distance from the true states) for these two maps, as well as for the lowest-order (Itô) map and two other higher-order maps. Our results show that, for a generic system, if the statistic $\phi_t$ can be extracted from experiment along with $I_t$, then the $\Phi$-map gives a smaller error than any other. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.10937 [quant-ph] (or arXiv:2601.10937v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.10937 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Nattaphong Wonglakhon [view email] [v1] Fri, 16 Jan 2026 01:46:56 UTC (1,673 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum trajectories for time-binned data and their closeness to fully conditioned quantum trajectories, by Nattaphong Wonglakhon and Areeya Chantasri and Howard M. WisemanView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?)