Parameter estimation for quantum jump unraveling
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AbstractWe consider the estimation of parameters encoded in the measurement record of a continuously monitored quantum system in the jump unraveling, corresponding to a single-shot scenario, where information is continuously gathered. Here, it is generally difficult to assess the precision of the estimation procedure via the Fisher Information due to intricate temporal correlations and memory effects. In this paper we provide a full set of solutions to this problem. First, for multi-channel renewal processes we relate the Fisher Information to an underlying Markov chain and derive a easily computable expression for it. For non-renewal processes, we introduce a new algorithm that combines two methods: the monitoring operator method for metrology and the Gillespie algorithm which allows for efficient sampling of a stochastic form of the Fisher Information along individual quantum trajectories. We show that this stochastic Fisher Information satisfies useful properties related to estimation on a single run. Finally, we consider the case where some information is lost in data compression/post-selection and provide tools for computing the Fisher Information in this case. All scenarios are illustrated with instructive examples from quantum optics and condensed matter.► BibTeX data@article{Radaelli2026parameterestimation, doi = {10.22331/q-2026-02-02-1993}, url = {https://doi.org/10.22331/q-2026-02-02-1993}, title = {Parameter estimation for quantum jump unraveling}, author = {Radaelli, Marco and Smiga, Joseph A. and Landi, Gabriel T. and Binder, Felix C.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {1993}, month = feb, year = {2026} }► References [1] Lewis A. Clark, Adam Stokes, and Almut Beige, Phys. Rev. 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A, 109 012214 (2024), 10.1103/PhysRevA.109.012214. https://doi.org/10.1103/PhysRevA.109.012214Cited byCould not fetch Crossref cited-by data during last attempt 2026-02-02 10:50:38: Could not fetch cited-by data for 10.22331/q-2026-02-02-1993 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-02-02 10:50:38: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractWe consider the estimation of parameters encoded in the measurement record of a continuously monitored quantum system in the jump unraveling, corresponding to a single-shot scenario, where information is continuously gathered. Here, it is generally difficult to assess the precision of the estimation procedure via the Fisher Information due to intricate temporal correlations and memory effects. In this paper we provide a full set of solutions to this problem. First, for multi-channel renewal processes we relate the Fisher Information to an underlying Markov chain and derive a easily computable expression for it. For non-renewal processes, we introduce a new algorithm that combines two methods: the monitoring operator method for metrology and the Gillespie algorithm which allows for efficient sampling of a stochastic form of the Fisher Information along individual quantum trajectories. We show that this stochastic Fisher Information satisfies useful properties related to estimation on a single run. Finally, we consider the case where some information is lost in data compression/post-selection and provide tools for computing the Fisher Information in this case. All scenarios are illustrated with instructive examples from quantum optics and condensed matter.► BibTeX data@article{Radaelli2026parameterestimation, doi = {10.22331/q-2026-02-02-1993}, url = {https://doi.org/10.22331/q-2026-02-02-1993}, title = {Parameter estimation for quantum jump unraveling}, author = {Radaelli, Marco and Smiga, Joseph A. and Landi, Gabriel T. and Binder, Felix C.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {1993}, month = feb, year = {2026} }► References [1] Lewis A. Clark, Adam Stokes, and Almut Beige, Phys. Rev. A, 99 022102 (2019), 10.1103/PhysRevA.99.022102. https://doi.org/10.1103/PhysRevA.99.022102 [2] K. Micadei, D. A. Rowlands, F. A. Pollock, L. C. Céleri, R. M. Serra, and K. Modi, New J. Phys., 17 023057 (2015), 10.1088/1367-2630/17/2/023057. https://doi.org/10.1088/1367-2630/17/2/023057 [3] Paul M. 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Cover and Joy A. Thomas, Elements of information theory, Wiley (1991). [20] Marco Radaelli, Gabriel T. Landi, and Felix C. Binder, Phys. Rev. A, 110 062212 (2024), 10.1103/PhysRevA.110.062212. https://doi.org/10.1103/PhysRevA.110.062212 [21] Daniel T. Gillespie, J. Comput. Phys., 22 403–434 (1976), 10.1016/0021-9991(76)90041-3. https://doi.org/10.1016/0021-9991(76)90041-3 [22] Daniel T. Gillespie, J. Phys. Chem., 81 2340–2361 (1977), 10.1021/j100540a008. https://doi.org/10.1021/j100540a008 [23] Marco Radaelli, Fisher–Gillespie algorithm in Julia (2024). https://github.com/marcoradaelli/WaitingTimeMetrology [24] Steven M. Kay, Fundamentals of statistical signal processing: estimation theory, Prentice-Hall (1993). [25] Rafał Demkowicz-Dobrzański, Wojciech Górecki, and Mădălin Guţă, J. Phys. A Math. Theor., 53 363001 (2020), 10.1088/1751-8121/ab8ef3. https://doi.org/10.1088/1751-8121/ab8ef3 [26] Harry L. Van Trees, Detection, estimation, and modulation theory, John Wiley & Sons (2004). 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