Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2203.10137

Optimal Dose-Limited Phase Estimation without Entanglement

Stewart A. Koppell, Mark A. Kasevich

Published Mar 18, 2022• 3 citations
arXivHTMLPDF

Abstract

Phase estimation is one of the most important facets of quantum metrology, with applications in sensing, microscopy, and quantum computation. When estimating a phase shift in a lossy medium, there is an upper bound on the attainable information per particle sent through the phase shift. Previously, only entanglement-enhanced measurements have been shown to saturate this bound. We introduce a measurement scheme which can saturate the bound without relying on entanglement.

DOI
10.48550/arxiv.2203.10137

Related papers

Optimal Quantum Measurements for Phase Estimation

Barry C. Sanders, Gerard J Milburn

Quantum information theory is applied to practical interferometer-based phase measurements to deduce the optimal phase measurement scheme with two optical modes. Optimal phase measurements, given ideal input states, reveal an asymptotic $1/n$ decrease in phase uncertainty $\ensuremath{\Delta}\ensuremath{\theta}$ for $n$ the mean photon number of the input state. In contradistinction to previous schemes for realizing the number-phase uncertainty limit, the $1/n$ limit achieved here is independent of the interferometer phase shift; prior information about the expected phase shift is not necessary to attain this limit. These results apply more generally to su(2) and so(3) phase parameter estimation.

Physical Review Letters•Oct 16, 1995•242 citations

Dose-efficient Quantum Phase Estimation in Lossy Optical Interferometry

Qilin Yu, Ben Wang, Kaimin Zheng +3 more

Optical interferometry is a cornerstone technique for precise phase measurements across various fields. In many applications, for example, biological imaging, it often necessitates stringent limits on light intensity to prevent adverse effects on light-sensitive samples, a condition known as dose-limited regimes. Maximizing the precision per dose is therefore crucial. In quantum metrology, quantum correlations enable high precision in phase estimation while adhering to dose constraints. Nevertheless, photon loss, including absorption by a sample, substantially diminishes the benefits of quantum enhancement in interferometry. In this work, we experimentally investigate a dose-efficient approach to quantum phase estimation using sequential strategies in the presence of loss. Performance of sequential strategies with and without control is evaluated through quantum Fisher information (QFI) per dose. Experimental results show that both sequential strategies exceed the classical limit and outperform the parallel strategy using unbalanced N00N states. Notably, the control-enhanced sequential strategy attains superior QFI per dose, approaching the quantum limit. These results highlight the promise of sequential strategy for imaging and sensing in resource-constrained scenarios, marking a significant step toward practical and efficient quantum metrology in lossy environments.

quant-pharXiv:2606.14254•Optica•Jun 15, 2026•0 citations

Optimal Measurements for Simultaneous Quantum Estimation of Multiple Phases

Luca Pezzè, Mario Arnolfo Ciampini, Nicolò Spagnolo +6 more

A quantum theory of multiphase estimation is crucial for quantum-enhanced sensing and imaging and may link quantum metrology to more complex quantum computation and communication protocols. In this Letter, we tackle one of the key difficulties of multiphase estimation: obtaining a measurement which saturates the fundamental sensitivity bounds. We derive necessary and sufficient conditions for projective measurements acting on pure states to saturate the ultimate theoretical bound on precision given by the quantum Fisher information matrix. We apply our theory to the specific example of interferometric phase estimation using photon number measurements, a convenient choice in the laboratory. Our results thus introduce concepts and methods relevant to the future theoretical and experimental development of multiparameter estimation.

arXiv:1705.03687•Physical Review Letters•Sep 29, 2017•199 citations

Precise Phase Measurements using an Entangled Coherent State

Paul Knott, Jacob Dunningham

Quantum entanglement offers the possibility of making measurements beyond the classical limit, however some issues still need to be overcome before it can be applied in realistic lossy systems. Recent work has used the quantum Fisher information (QFI) to show that entangled coherent states (ECSs) may be useful for this purpose as they combine sub-classical phase precision capabilities with robustness (Joo et al., 2011). However, to date no effective scheme for measuring a phase in lossy systems using an ECS has been devised. Here we present a scheme that does just this. We show how one could measure a phase to a precision significantly better than that attainable by both unentangled "classical" states and highly-entangled NOON states over a wide range of different losses. This brings quantum metrology closer to being a realistic and practical technology.

arXiv:1401.3969•Jan 16, 2014•0 citations

Ultimate sensitivity of multiparameter estimation in quantum sensing with undetected photons

Sanjeet Swaroop Panda, Lorcan O. Conlon, Li Gong +4 more

Quantum sensing with undetected photons is a technique where photons of one wavelength probe a sample, but information is extracted by measuring photons of another wavelength that never interacts with the sample. This has seen significant experimental advances in applications such as spectroscopy, microscopy, and bio-sensing. However, a detailed theoretical analysis using the tools of quantum metrology is currently lacking. Thus it is unclear how far away current schemes are from fundamental limits, and what the optimal measurement strategies are. We apply a multiparameter quantum estimation framework to quantify the error when estimating the unknown transmission and phase shift of a sample. The optimal measurement scheme is shown to require only a single controllable phase shift, easily implementable in existing setups. We also study how to use multipass interactions to maximise information gain. In general the optimum number of passes scales inversely with the log of the transmission of the sample. This work clarifies the metrological power of quantum sensing with undetected photons, and provides guidance for the design of experiments requiring high sensitivity.

quant-pharXiv:2604.19120•Apr 22, 2026•0 citations

Entanglement-Enhanced Measurement of a Completely Unknown Phase

Dominic William Berry, Guo‐Yong Xiang, Brendon L. Higgins +2 more

We demonstrate a method for achieving phase measurements with accuracy beyond the standard quantum limit using entangled states. A sophisticated feedback scheme means that no initial estimate of the phase is required.

Conference on Lasers and Electro-Optics•Jan 1, 2010•0 citations
Phase estimation is one of the most important facets of quantum metrology, with applications in sensing, microscopy, and quantum computation. When estimating a phase shift in a lossy medium, there is an upper bound on the attainable information per particle sent through the phase shift. Previously, only entanglement-enhanced measurements have been shown to saturate this bound. We introduce a measurement scheme which can saturate the bound without relying on entanglement.
Quantum information theory is applied to practical interferometer-based phase measurements to deduce the optimal phase measurement scheme with two optical modes. Optimal phase measurements, given ideal input states, reveal an asymptotic 1/n1/n1/n decrease in phase uncertainty $\ensuremath{\Delta}\ensuremath{\theta}$ for nnn the mean photon number of the input state. In contradistinction to previous schemes for realizing the number-phase uncertainty limit, the 1/n1/n1/n limit achieved here is independent of the interferometer phase shift; prior information about the expected phase shift is not necessary to attain this limit. These results apply more generally to su(2) and so(3) phase parameter estimation.
Optical interferometry is a cornerstone technique for precise phase measurements across various fields. In many applications, for example, biological imaging, it often necessitates stringent limits on light intensity to prevent adverse effects on light-sensitive samples, a condition known as dose-limited regimes. Maximizing the precision per dose is therefore crucial. In quantum metrology, quantum correlations enable high precision in phase estimation while adhering to dose constraints. Nevertheless, photon loss, including absorption by a sample, substantially diminishes the benefits of quantum enhancement in interferometry. In this work, we experimentally investigate a dose-efficient approach to quantum phase estimation using sequential strategies in the presence of loss. Performance of sequential strategies with and without control is evaluated through quantum Fisher information (QFI) per dose. Experimental results show that both sequential strategies exceed the classical limit and outperform the parallel strategy using unbalanced N00N states. Notably, the control-enhanced sequential strategy attains superior QFI per dose, approaching the quantum limit. These results highlight the promise of sequential strategy for imaging and sensing in resource-constrained scenarios, marking a significant step toward practical and efficient quantum metrology in lossy environments.
A quantum theory of multiphase estimation is crucial for quantum-enhanced sensing and imaging and may link quantum metrology to more complex quantum computation and communication protocols. In this Letter, we tackle one of the key difficulties of multiphase estimation: obtaining a measurement which saturates the fundamental sensitivity bounds. We derive necessary and sufficient conditions for projective measurements acting on pure states to saturate the ultimate theoretical bound on precision given by the quantum Fisher information matrix. We apply our theory to the specific example of interferometric phase estimation using photon number measurements, a convenient choice in the laboratory. Our results thus introduce concepts and methods relevant to the future theoretical and experimental development of multiparameter estimation.
Quantum entanglement offers the possibility of making measurements beyond the classical limit, however some issues still need to be overcome before it can be applied in realistic lossy systems. Recent work has used the quantum Fisher information (QFI) to show that entangled coherent states (ECSs) may be useful for this purpose as they combine sub-classical phase precision capabilities with robustness (Joo et al., 2011). However, to date no effective scheme for measuring a phase in lossy systems using an ECS has been devised. Here we present a scheme that does just this. We show how one could measure a phase to a precision significantly better than that attainable by both unentangled "classical" states and highly-entangled NOON states over a wide range of different losses. This brings quantum metrology closer to being a realistic and practical technology.
Quantum sensing with undetected photons is a technique where photons of one wavelength probe a sample, but information is extracted by measuring photons of another wavelength that never interacts with the sample. This has seen significant experimental advances in applications such as spectroscopy, microscopy, and bio-sensing. However, a detailed theoretical analysis using the tools of quantum metrology is currently lacking. Thus it is unclear how far away current schemes are from fundamental limits, and what the optimal measurement strategies are. We apply a multiparameter quantum estimation framework to quantify the error when estimating the unknown transmission and phase shift of a sample. The optimal measurement scheme is shown to require only a single controllable phase shift, easily implementable in existing setups. We also study how to use multipass interactions to maximise information gain. In general the optimum number of passes scales inversely with the log of the transmission of the sample. This work clarifies the metrological power of quantum sensing with undetected photons, and provides guidance for the design of experiments requiring high sensitivity.