Super-Exponential Advantage of Squeezed Light in Phase Estimation under Discrete Phase Randomisation
Abstract
A paradigmatic task in quantum metrology is that of phase estimation. For this task it is commonly believed, under reasonable assumptions about prior information, that a quadratic advantage in sensitivity is the maximum possible advantage offered by the use of quantum resources. In this work, we consider a channel that implements a phase shift by an angle 2πk/M, where k is a uniformly random unknown integer, in addition to a small unknown phase shift of interest. We show that, subject to a constraint on the mean photon number per channel use, there is a super-exponential separation between the quantum Fisher information (QFI) attainable using a squeezed vacuum state and that attainable using coherent states. This advantage holds over any state obtained from a coherent state via phase covariant channels. Specifically, when the mean photon number per channel use is 1, the ratio of their QFI grows as Ω[(M/√2e)M]. For a mean photon number per channel use of M/log(M), the squeezed vacuum QFI is Ω(M3/2/√(log(M))), whereas for a coherent state it is at most exp[−Mloglog(M)+O(M)]. We complement this QFI analysis with non-asymptotic estimation results. For a mean photon number per channel use of M/log M, an explicit squeezed-vacuum protocol estimates the phase to accuracy O(1/M) using O(√(Mlog M)) channel uses, whereas every coherent state protocol requires at least exp[Mloglog M−O(M)] channel uses. We consider the effects of noise and show that the ratio of their QFIs can still grow super-exponentially in M. Finally, under fixed optical loss and thermal noise, choosing n̅=M2/(log M)3/2 allows squeezed vacuum with heterodyne detection to achieve accuracy O(1/M) using sub-polynomially many channel uses, whereas every protocol in the specified classical family requires super-polynomially many.
Related
- Quantum metrological advantage of high-order squeezed states
- Exponential advantage in continuous-variable quantum state learning
- Exponential Entanglement Advantage in Sensing Correlated Noise
- An Exponential Sample-Complexity Advantage for Coherent Quantum Inference
- Exponential Quantum Advantage in Numbers-on-Forehead Communication
BibTeX
@misc{conlon2026superexponential,
title = {{Super-Exponential Advantage of Squeezed Light in Phase Estimation under Discrete Phase Randomisation}},
author = {Lorcan O. Conlon and V Vijendran and Aritra Das and Yu-Xin Wang and Erfan Abbasgholinejad and Anthony J. Brady and Jacob Bringewatt and Sean R. Muleady and Syed M. Assad and Alexey V. Gorshkov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03657},
eprint = {2610.03657},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03657},
}
RIS
TY - UNPB
TI - Super-Exponential Advantage of Squeezed Light in Phase Estimation under Discrete Phase Randomisation
AU - Lorcan O. Conlon
AU - V Vijendran
AU - Aritra Das
AU - Yu-Xin Wang
AU - Erfan Abbasgholinejad
AU - Anthony J. Brady
AU - Jacob Bringewatt
AU - Sean R. Muleady
AU - Syed M. Assad
AU - Alexey V. Gorshkov
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03657
UR - https://arxiv.org/abs/2610.03657
AB - A paradigmatic task in quantum metrology is that of phase estimation. For this task it is commonly believed, under reasonable assumptions about prior information, that a quadratic advantage in sensitivity is the maximum possible advantage offered by the use of quantum resources. In this work, we consider a channel that implements a phase shift by an angle 2πk/M, where k is a uniformly random unknown integer, in addition to a small unknown phase shift of interest. We show that, subject to a constraint on the mean photon number per channel use, there is a super-exponential separation between the quantum Fisher information (QFI) attainable using a squeezed vacuum state and that attainable using coherent states. This advantage holds over any state obtained from a coherent state via phase covariant channels. Specifically, when the mean photon number per channel use is 1, the ratio of their QFI grows as Ω[(M/√2e)^M]. For a mean photon number per channel use of M/log(M), the squeezed vacuum QFI is Ω(M^3/2/√(log(M))), whereas for a coherent state it is at most exp[−Mloglog(M)+O(M)]. We complement this QFI analysis with non-asymptotic estimation results. For a mean photon number per channel use of M/log M, an explicit squeezed-vacuum protocol estimates the phase to accuracy O(1/M) using O(√(Mlog M)) channel uses, whereas every coherent state protocol requires at least exp[Mloglog M−O(M)] channel uses. We consider the effects of noise and show that the ratio of their QFIs can still grow super-exponentially in M. Finally, under fixed optical loss and thermal noise, choosing n̅=M^2/(log M)^3/2 allows squeezed vacuum with heterodyne detection to achieve accuracy O(1/M) using sub-polynomially many channel uses, whereas every protocol in the specified classical family requires super-polynomially many.
ER -