On the Quantumness of Multiparameter Estimation Problems for Qubit Systems

Razavian, Sholeh; Paris, Matteo G. A.; Genoni, Marco G.

doi:10.3390/e22111197

Cited by 25 publications

(21 citation statements)

References 62 publications

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“…Generally, the multi-parameter estimation protocol is harder than the single-parameter estimation protocol since we cannot always achieve the optimal estimation of multiple parameters simultaneously encrypted in a given quantum system. This is mainly due to the incompatibility of quantum measurements [82]. Consequently, the quantum limits of accuracy cannot usually be achieved.…”

Section: Quantum Fisher Information Matrix Via Vectorization Methodsmentioning

confidence: 99%

Analytical techniques in single and multi-parameter quantum estimation theory: a focused review

Slaoui¹,

Drissi²,

Saidi³

et al. 2022

Preprint

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As we enter the era of quantum technologies, quantum estimation theory provides an operationally motivating framework for determining high precision devices in modern technological applications. The aim of any estimation process is to extract information from an unknown parameter embedded in a physical system such as the estimation converges to the true value of the parameter. According to the Cramér-Rao inequality in mathematical statistics, the Fisher information in the case of single-parameter estimation procedures, and the Fisher information matrix in the case of multi-parameter estimation, are the key quantities representing the ultimate precision of the parameters specifying a given statistical model. In quantum estimation strategies, it is usually difficult to derive the analytical expressions of such quantities in a given quantum state. This review provides comprehensive techniques on the analytical calculation of the quantum Fisher information as well as the quantum Fisher information matrix in various scenarios and via several methods. Furthermore, it provides a mathematical transition from classical to quantum estimation theory applied to many freedom quantum systems. To clarify these results, we examine these developments using some examples. Other challenges, including their links to quantum correlations and saturating the quantum Cramér-Rao bound, are also addressed.

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Section: Quantum Fisher Information Matrix Via Vectorization Methodsmentioning

confidence: 99%

Analytical techniques in single and multi-parameter quantum estimation theory: a focused review

Slaoui¹,

Drissi²,

Saidi³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…is equal to the Holevo Cramér-Rao bound and thus asymptotically attainable [49,72]. Therefore, thanks to the equality between the complex matrices (25), this condition can be checked from the optimal purification.…”

Section: Purification-based Definition Of the Qfi Matrixmentioning

confidence: 96%

“…For the parameters that characterize a quantum state (quantum state estimation), the main roadblock is essentially measurement incompatibility, related with the impossibility of simultaneous measurement of noncommuting observables. This issue has been studied for decades, [13][14][15][16][17], from seminal studies [14,18,19] to more recent developments [20][21][22][23][24][25][26][27][28]. Interestingly, in the asymptotic setting and allowing for collective measurements on identical copies [29][30][31], measurement incompatibility can at most double the total mean squared error on the parameters' estimates [32,33].…”

Section: Introductionmentioning

confidence: 99%

Probe incompatibility in multiparameter noisy quantum metrology

Albarelli,

Demkowicz-Dobrzanski

2021

Preprint

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We derive fundamental bounds on the maximal achievable precision in multiparameter noisy quantum channel estimation, valid under the most general entanglement-assisted adaptive strategy, which are tighter than the bounds obtained by a direct use of single-parameter bounds. This allows us to study the issue of the optimal probe incompatibility in the simultaneous estimation of multiple parameters in generic noisy channels, while so far the issue has been studied mostly in effectively noiseless scenarios (where the Heisenberg scaling is possible). We apply our results to the estimation of both unitary and noise parameters, and indicate models where the fundamental probe incompatibility is present. In particular, we show that in lossy multiple arm interferometry the probe incompatibility is as strong as in the noiseless scenario. Finally, going beyond the multiple-parameter estimation paradigm, we introduce the concept of random quantum sensing and show how the tools developed may be applied to multiple channels discrimination problems. As an illustration, we provide a simple proof of the loss of the quadratic advantage of time-continuous Grover algorithm in presence of dephasing or erasure noise.

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“…Differently from the single-parameter case, in the multiparameter scenario the quantum limit given by the matrix inequality (4) is not achievable in general [45,[52][53][54][55][56][57]. This fact has its root in the non-commuting nature of the operator algebra, preventing the simultaneous measurement of arbitrary observables with arbitrary accuracy and leading to trade offs for the precision of the individual estimators.…”

Section: Multi-parameter Quantum Estimationmentioning

confidence: 99%

Multi-parameter quantum metrology with discrete-time quantum walks

Annabestani,

Hassani,

Tamascelli

et al. 2021

Preprint

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We address multi-parameter quantum estimation for one-dimensional discrete-time quantum walks and its applications to quantum metrology. We use the quantum walker as a probe for unknown parameters encoded on its coin degrees of freedom. We find an analytic expression of the quantum Fisher information matrix for the most general coin operator, and show that only two out of the three coin parameters can be accessed. We also prove that the resulting two-parameter coin model is asymptotically classical i.e. the Uhlmann curvature vanishes. Finally, we apply our findings to relevant case studies, including the simultaneous estimation of charge and mass in the discretized Dirac model.

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On the Quantumness of Multiparameter Estimation Problems for Qubit Systems

Cited by 25 publications

References 62 publications

Analytical techniques in single and multi-parameter quantum estimation theory: a focused review

Analytical techniques in single and multi-parameter quantum estimation theory: a focused review

Probe incompatibility in multiparameter noisy quantum metrology

Multi-parameter quantum metrology with discrete-time quantum walks

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