Super-Exponential Advantage of Squeezed Light in Phase Estimation under Discrete Phase Randomisation
Year: 2026
Type: preprint
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 $Ω[(M/\sqrt{2}e)^M]$. For a mean photon number per channel use of $M/\log(M)$, the squeezed vacuum QFI is $Ω(M^{3/2}/\sqrt{\log(M)})$, whereas for a coherent state it is at most $\exp[-M\log\log(M)+O(M)]$. 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 $O(\sqrt{M\log M})$ channel uses, whereas every coherent state protocol requires at least $\exp[M\log\log M-O(M)]$ 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 $\bar n=M^2/(\log M)^{3/2}$ 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.
Source: arXiv (Cornell University)
Institutions: National Institute of Standards and Technology, Joint Center for Quantum Information and Computer Science, Joint Quantum Institute, University of Maryland, College Park, Agency for Science, Technology and Research, Centre for Quantum Technologies, National University of Singapore, University of Technology Sydney, IonQ (United States), United States Naval Academy
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220416556