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, $N_\mathrm{RMS}$, 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.

arXiv:2611.06645 [quant-ph]

(or arXiv:2611.06645v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2611.06645 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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