Multi-parameter estimation beyond quantum Fisher information

Demkowicz-Dobrzański, Rafał; Górecki, Wojciech; Guţǎ, Mădălin

doi:10.1088/1751-8121/ab8ef3

Cited by 143 publications

(160 citation statements)

References 155 publications

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“…First, the widely used quantum Cramér-Rao (CR) bound for multiple parameters is not in general saturable, due to the incompatibility of the optimal measurements for different parameters [49,51,52]. Therefore, unlike in the single-parameter case, the quantum Fisher information (QFI) does not provide the full insight into the problem [51,[57][58][59][60]. On the other hand, stronger bounds, such as the HCR bound [59][60][61][62][63][64], have no closed-form expressions (except for specific cases [65]).…”

Section: Umentioning

confidence: 99%

Optimal probes and error-correction schemes in multi-parameter quantum metrology

Górecki

Zhou

Jiang

et al. 2020

Quantum

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We derive a necessary and sufficient condition for the possibility of achieving the Heisenberg scaling in general adaptive multi-parameter estimation schemes in presence of Markovian noise. In situations where the Heisenberg scaling is achievable, we provide a semidefinite program to identify the optimal quantum error correcting (QEC) protocol that yields the best estimation precision. We overcome the technical challenges associated with potential incompatibility of the measurement optimally extracting information on different parameters by utilizing the Holevo Cramér-Rao (HCR) bound for pure states. We provide examples of significant advantages offered by our joint-QEC protocols, that sense all the parameters utilizing a single error-corrected subspace, over separate-QEC protocols where each parameter is effectively sensed in a separate subspace.

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Section: Umentioning

confidence: 99%

Optimal probes and error-correction schemes in multi-parameter quantum metrology

Górecki

Zhou

Jiang

et al. 2020

Quantum

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“…While a general framework for Bayesian quantum multiparameter estimation exists (see ref. 41 for a complete review), there are several remaining open questions. In particular, the operational application of optimal strategies, measurements and probes preparation, is a field that needs to be largely explored, even if some theoretical results are available also in the limited data regime 44 .…”

Section: Discussionmentioning

confidence: 99%

“…In general, the saturable bounds for quantum multiparameter strategies are not as defined as in the single-parameter case, and trade-offs in the achievable precision for each of the parameters have to be sought [35][36][37][38][39] . Different theoretical works have studied a non-asymptotic Bayesian approach in quantum multiparameter estimation [40][41][42][43][44] , thus providing bounds and protocols to generally address limiteddata quantum metrology.…”

Section: Introductionmentioning

confidence: 99%

Experimental adaptive Bayesian estimation of multiple phases with limited data

et al. 2020

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Achieving ultimate bounds in estimation processes is the main objective of quantum metrology. In this context, several problems require measurement of multiple parameters by employing only a limited amount of resources. To this end, adaptive protocols, exploiting additional control parameters, provide a tool to optimize the performance of a quantum sensor to work in such limited data regime. Finding the optimal strategies to tune the control parameters during the estimation process is a non-trivial problem, and machine learning techniques are a natural solution to address such task. Here, we investigate and implement experimentally an adaptive Bayesian multiparameter estimation technique tailored to reach optimal performances with very limited data. We employ a compact and flexible integrated photonic circuit, fabricated by femtosecond laser writing, which allows to implement different strategies with high degree of control. The obtained results show that adaptive strategies can become a viable approach for realistic sensors working with a limited amount of resources.

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“…In this section, we will provide all the basic notions of multi-parameter quantum metrology that are needed for our goals. We refer to the following references [ 12 , 13 , 14 , 15 ] for more explanations and technical details on this topic.…”

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

confidence: 99%

“…As a matter of fact, there are several problems of interest that are inherently involving more than one parameter [ 12 , 13 , 14 , 15 ], e.g. estimation of unitary operations and of multiple phases [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ], estimation of phase and noise [ 27 , 28 , 29 , 30 ], and superresolution of incoherent sources [ 31 , 32 , 33 ].…”

Section: Introductionmentioning

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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Multi-parameter estimation beyond quantum Fisher information

Cited by 143 publications

References 155 publications

Optimal probes and error-correction schemes in multi-parameter quantum metrology

Optimal probes and error-correction schemes in multi-parameter quantum metrology

Experimental adaptive Bayesian estimation of multiple phases with limited data

On the Quantumness of Multiparameter Estimation Problems for Qubit Systems

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