Local versus global strategies in multiparameter estimation

Knott, P. A.; Proctor, Timothy; Hayes, Anthony Joseph; Ralph, Jason F.; Kok, Pieter; Dunningham, J. A.

doi:10.1103/physreva.94.062312

Cited by 80 publications

(136 citation statements)

References 33 publications

Supporting

Mentioning

133

Contrasting

Order By: Relevance

“…Interestingly, Ref. [166] has succeeded in showing that, if the phase shifts are reparametrised as phase differences between consecutive arms, the same precision can be attained by means of local as well as global estimation strategies.…”

Section: Quantum Phase Imagingmentioning

confidence: 99%

A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging

et al. 2020

View full text Add to dashboard Cite

The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such multiparameter estimation can be achieved depends on understanding the many subtleties that come into play: establishing solid foundations is key to delivering future technology for this task. In this article we discuss the state of the art of quantum multiparameter estimation, with a particular emphasis on its theoretical tools, on application to imaging problems, and on the possible avenues towards the next developments.

show abstract

Section: Quantum Phase Imagingmentioning

confidence: 99%

A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Similarly, the estimation precision of n optical phase differences can be enhanced by using an n-mode entangled state as input in a multi-mode interferometer [87][88][89] . However, this precision enhancement has also been matched using separable states with equal number of modes 90 . This has been demonstrated theoretically for spatial distinguishability of different light emitters 91 .…”

Section: H Non-entangling Strategiesmentioning

confidence: 99%

Geometric perspective on quantum parameter estimation

Sidhu

Kok

2020

AVS Quantum Science

185

132

View full text Add to dashboard Cite

Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this review, we collect some of the key theoretical results in quantum parameter estimation by presenting the theory for the quantum estimation of a single parameter, multiple parameters, and optical estimation using Gaussian states. We give an overview of results in areas of current research interest, such as Bayesian quantum estimation, noisy quantum metrology, and distributed quantum sensing. We address the question how minimum measurement errors can be achieved using entanglement as well as more general quantum states. This review is presented from a geometric perspective. This has the advantage that it unifies a wide variety of estimation procedures and strategies, thus providing a more intuitive big picture of quantum parameter estimation. CONTENTS

show abstract

“…( )because the quantum Fisher information for path-symmetric pure states can be rewritten as F n 1 1 [47,52]. Therefore, we can control the asymptotic performance by changing  and  .…”

Section: The Role Of Intra-mode and Inter-mode Correlations For A Lowmentioning

confidence: 99%

Quantum metrology in the presence of limited data

Rubio

Dunningham

2019

New J. Phys.

View full text Add to dashboard Cite

Quantum metrology protocols are typically designed around the assumption that we have an abundance of measurement data, but recent practical applications are increasingly driving interest in cases with very limited data. In this regime the best approach involves an interesting interplay between the amount of data and the prior information. Here we propose a new way of optimising these schemes based on the practically-motivated assumption that we have a sequence of identical and independent measurements. For a given probe state we take our measurement to be the best one for a single shot and we use this sequentially to study the performance of different practical states in a Mach-Zehnder interferometer when we have moderate prior knowledge of the underlying parameter. We find that we recover the quantum Cramér-Rao bound asymptotically, but for low data counts we find a completely different structure. Despite the fact that intra-mode correlations are known to be the key to increasing the asymptotic precision, we find evidence that these could be detrimental in the low data regime and that entanglement between the paths of the interferometer may play a more important role. Finally, we analyse how close realistic measurements can get to the bound and find that measuring quadratures can improve upon counting photons, though both strategies converge asymptotically. These results may prove to be important in the development of quantum enhanced metrology applications where practical considerations mean that we are limited to a small number of trials.the experiment enough times and that we have certain prior knowledge about the unknown parameter 2 [4,5,18,19] (see footnote 2), and this simplifies the optimisation of the error considerably. Furthermore, the Fisher information has a certain fundamental character. In particular, it can be seen as a distinguishability metric [20] that arises in the expansion of the Bures distance between two infinitesimally close states [3,18]. Moreover, its reciprocal gives us the asymptotic limit for the Bayesian mean square error as a function of the number of repetitions under some fairly general assumptions 3 [5] (see footnote 3), and this is also the case for other approaches that are more conservative than the Cramér-Rao bound too [21,22].Nevertheless, the fact that this technique normally requires many repetitions to be useful is an important drawback to study realistic physical systems such as those previously mentioned. This problem has already been acknowledged in the literature (e.g. in [4, 5, 18, 27]), and several solutions have been proposed. A conceptually simple and straightforward approach consists in using a general measure of uncertainty and estimating how many measurements are needed such that the results predicted by the asymptotic theory are valid, which can always be done numerically [5,28]. In addition, we can rely on numerical techniques such as Monte Carlo simulations [29] or machine learning [30] to perform the optimisation directly, or can simply examine the behavi...

show abstract

Local versus global strategies in multiparameter estimation

Cited by 80 publications

References 33 publications

A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging

A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging

Geometric perspective on quantum parameter estimation

Quantum metrology in the presence of limited data

Contact Info

Product

Resources

About