Parameter estimation for quantum jump unraveling

Marco Radaelli; Joseph A. Smiga; Gabriel T. Landi; Felix C. Binder

doi:10.22331/q-2026-02-02-1993

Parameter estimation for quantum jump unraveling

Marco Radaelli^1,2, Joseph A. Smiga³, Gabriel T. Landi³, and Felix C. Binder^1,2

¹School of Physics, Trinity College Dublin, Dublin 2, Ireland
²Trinity Quantum Alliance, Unit 16, Trinity Technology and Enterprise Centre, Pearse Street, Dublin 2, Ireland
³Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA

Published:	2026-02-02, volume 10, page 1993
Editor:	Luis A. Correa
Eprint:	arXiv:2402.06556v2
Doi:	https://doi.org/10.22331/q-2026-02-02-1993
Citation:	Quantum 10, 1993 (2026).

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Abstract

We 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}
}

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[6] Saulo V. Moreira, Marco Radaelli, Alessandro Candeloro, Felix C. Binder, and Mark T. Mitchison, "Precision bounds for multiple currents in open quantum systems", Physical Review E 111 6, 064107 (2025).

[7] Gideon Lee, Ron Belyansky, Liang Jiang, and Aashish A. Clerk, "Timescales, Squeezing and Heisenberg Scalings in Many-Body Continuous Sensing", arXiv:2505.04591, (2025).

[8] Calum A. Brown, Katarzyna Macieszczak, and Robert L. Jack, "Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories?", Quantum 9, 1787 (2025).

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[16] Chattamas Manoworakul, Jason F. Ralph, Nattaphong Wonglakhon, and Areeya Chantasri, "Time-dependent multiparameter estimation for quantum experiments via online-offline sequential Monte-Carlo method", arXiv:2607.02987, (2026).

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