Ultimate precision of joint quadrature parameter estimation with a Gaussian probe

Bradshaw, Mark; Lam, Ping Koy; Assad, Syed M.

doi:10.1103/physreva.97.012106

Cited by 43 publications

(54 citation statements)

References 46 publications

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“…This is due to the non-trivial optimisation over a set of observables and the implementation of global measurements is a difficult task. However, few results that use the do exist for qubit state estimation 125 , two-parameter estimation with pure states 12 and two-parameter displacement estimation with twomode Gaussian states 126,127 . A recent study by Albarelli et al have investigated the numerical tractability of calculating the for multi-parameter estimation problems 128 .…”

Section: Saturating the Quantum Cramér-rao Boundmentioning

confidence: 99%

Geometric perspective on quantum parameter estimation

Sidhu

Kok

2020

AVS Quantum Science

186

132

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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

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Section: Saturating the Quantum Cramér-rao Boundmentioning

confidence: 99%

Geometric perspective on quantum parameter estimation

Sidhu

Kok

2020

AVS Quantum Science

186

132

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“…If the quantum statistical model does not fall into these classes, the evaluation of

may be unfeasible. Several efforts have been made in the literature in order to obtain numerical or even analytical results, at least for some specific classes of quantum states [ 26 , 28 , 56 , 57 , 58 , 59 , 60 , 61 ]. In particular, a closed formula has been derived for all single-qubit two-parameter quantum statistical models [ 43 ].…”

Section: Multi-parameter Quantum Metrology and A Measure Of mentioning

confidence: 99%

On the Quantumness of Multiparameter Estimation Problems for Qubit Systems

Razavian

Paris

Genoni

2020

Entropy

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The estimation of more than one parameter in quantum mechanics is a fundamental problem with relevant practical applications. In fact, the ultimate limits in the achievable estimation precision are ultimately linked with the non-commutativity of different observables, a peculiar property of quantum mechanics. We here consider several estimation problems for qubit systems and evaluate the corresponding quantumnessR, a measure that has been recently introduced in order to quantify how incompatible the parameters to be estimated are. In particular, R is an upper bound for the renormalized difference between the (asymptotically achievable) Holevo bound and the SLD Cramér-Rao bound (i.e., the matrix generalization of the single-parameter quantum Cramér-Rao bound). For all the estimation problems considered, we evaluate the quantumness R and, in order to better understand its usefulness in characterizing a multiparameter quantum statistical model, we compare it with the renormalized difference between the Holevo and the SLD-bound. Our results give evidence that R is a useful quantity to characterize multiparameter estimation problems, as for several quantum statistical model, it is equal to the difference between the bounds and, in general, their behavior qualitatively coincide. On the other hand, we also find evidence that, for certain quantum statistical models, the bound is not in tight, and thus R may overestimate the degree of quantum incompatibility between parameters.

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“…Except for special cases involving qubits 46 or estimating Gaussian amplitudes 47,48 , in general the problem of finding the optimal measurement that minimises the sum of the mean squared error (MSE) in multiparameter estimation is a non-trivial problem. Instead, one resorts to finding bounds on these errors 49 .…”

Section: Introductionmentioning

confidence: 99%

“…The computation of the Holevo bound was recently cast as a semidefinite programme which has made it easy to compute. This was first performed for the Gaussian amplitude estimation problem 47 and was later generalised to an arbitrary model 53 . Furthermore, analytic expressions which upper and lower bound the Holevo bound have recently been found 54 .…”

Section: Introductionmentioning

confidence: 99%