Precision Limits and Non-Gaussian Advantage in Optical Phase Estimation under Preparation Constraints
Abstract
In optical quantum metrology, the scaling of the quantum Fisher information (QFI) with the mean photon number is a standard benchmark for relating precision to probe resources. For phase estimation, Heisenberg scaling corresponds to a quadratic growth of the QFI with the mean photon number, which Gaussian probes can approach. Interestingly, certain non-Gaussian probes can exhibit arbitrarily large QFI even at fixed mean photon number. Here, we clarify the resource requirements underlying this behavior by introducing a constraint that separates physically admissible states from inadmissible ones: an envelope on the photon-number distribution that arises naturally from the physical limitations of state-generation methods. Building on this constraint and considering pure single-mode probes, we define a resource quantity, NRMS, fixed by the preparation constraints, and derive a finite bound on the QFI whose Heisenberg scaling is attainable. We identify a genuine metrological advantage of non-Gaussian states over Gaussian probes subject to the same constraints. Finally, we illustrate these results with an optical preparation model based on a universal gate set.
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BibTeX
@misc{izquierdo2026precision,
title = {{Precision Limits and Non-Gaussian Advantage in Optical Phase Estimation under Preparation Constraints}},
author = {Víctor Izquierdo and Javier Lalueza-Puértolas},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06645},
eprint = {2611.06645},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06645},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Precision Limits and Non-Gaussian Advantage in Optical Phase Estimation under Preparation Constraints
AU - Víctor Izquierdo
AU - Javier Lalueza-Puértolas
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06645
UR - https://arxiv.org/abs/2611.06645
AB - In optical quantum metrology, the scaling of the quantum Fisher information (QFI) with the mean photon number is a standard benchmark for relating precision to probe resources. For phase estimation, Heisenberg scaling corresponds to a quadratic growth of the QFI with the mean photon number, which Gaussian probes can approach. Interestingly, certain non-Gaussian probes can exhibit arbitrarily large QFI even at fixed mean photon number. Here, we clarify the resource requirements underlying this behavior by introducing a constraint that separates physically admissible states from inadmissible ones: an envelope on the photon-number distribution that arises naturally from the physical limitations of state-generation methods. Building on this constraint and considering pure single-mode probes, we define a resource quantity, N_RMS, fixed by the preparation constraints, and derive a finite bound on the QFI whose Heisenberg scaling is attainable. We identify a genuine metrological advantage of non-Gaussian states over Gaussian probes subject to the same constraints. Finally, we illustrate these results with an optical preparation model based on a universal gate set.
ER -