Homodyne Unravelling and Parameter Estimation in Squeezed Thermal Baths
Abstract
We derive an alternative formulation of the stochastic master equation describing the evolution of quantum systems continuously measured via homodyne detection in a squeezed-thermal environment. This formulation allows us to identify two distinct collapse operators, corresponding respectively to the monitored and unmonitored channels, and to express the quantum state evolution directly in terms of Kraus-like operators. As a consequence, it facilitates the application of advanced numerical methods that account for higher-order corrections and discrete-time monitoring, and it also enables the efficient numerical evaluation of Cramér-Rao bounds in parameter estimation problems. To demonstrate the latter, we evaluate the Fisher information of the continuous homodyne monitoring for qubit frequency estimation in the presence of a squeezed-thermal bath. Our results show that exponential scaling of the steady-state Fisher information rate with squeezing is retained even at non-zero temperature.
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BibTeX
@misc{oconnor2026homodyne,
title = {{Homodyne Unravelling and Parameter Estimation in Squeezed Thermal Baths}},
author = {Eoin O'Connor and Francesco Albarelli and Marco G. Genoni},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37438},
eprint = {2610.37438},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37438},
}
RIS
TY - UNPB
TI - Homodyne Unravelling and Parameter Estimation in Squeezed Thermal Baths
AU - Eoin O'Connor
AU - Francesco Albarelli
AU - Marco G. Genoni
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37438
UR - https://arxiv.org/abs/2610.37438
AB - We derive an alternative formulation of the stochastic master equation describing the evolution of quantum systems continuously measured via homodyne detection in a squeezed-thermal environment. This formulation allows us to identify two distinct collapse operators, corresponding respectively to the monitored and unmonitored channels, and to express the quantum state evolution directly in terms of Kraus-like operators. As a consequence, it facilitates the application of advanced numerical methods that account for higher-order corrections and discrete-time monitoring, and it also enables the efficient numerical evaluation of Cramér-Rao bounds in parameter estimation problems. To demonstrate the latter, we evaluate the Fisher information of the continuous homodyne monitoring for qubit frequency estimation in the presence of a squeezed-thermal bath. Our results show that exponential scaling of the steady-state Fisher information rate with squeezing is retained even at non-zero temperature.
ER -