Compatibility in multiparameter quantum metrology

By Sammy Ragy, Marcin Jarzyna, Rafal Demkowicz-Dobrzanski. 2016

291 citations recorded by the source corpus.

Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of a single measurement optimally extracting information from the probe state on all the parameters, and (iii) statistical independence of the estimated parameters. We consider the situation when these concerns present no obstacle, and for every estimated parameter the variance obtained in the multiparameter scheme is equal to that of an optimal scheme for that parameter alone, assuming all other parameters are perfectly known. We call such models compatible. In establishing a rigorous theoretical framework for investigating compatibility, we clarify some ambiguities and inconsistencies present in the literature and discuss several examples to highlight interesting features of unitary and nonunitary parameter estimation, as well as deriving new bounds for physical problems of interest, such as the simultaneous estimation of phase and local dephasing.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/e8c3813a906ce61f3dfde1d7ef51a4fa26e344d2

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Geometry of quantum phase transitions (2019, background): “Within the comprehensive framework of quantum local asymptotic normality (QLAN) [328, 329, 330, 331], a necessary and sufficient condition for the saturation of the multi-parameter CRB is given byUμν = 0 for all μ and ν [190].”
Quantum-enhanced measurements without entanglement (2017, unknown): “…in terms of the symmetric logarithmic derivatives Lρθk and Lρθk′ , the corresponding quantum Fisher information matrix element is de- fined as Iθk,θk′ ≡ Re [ Tr ( ρθLρθkLρθk′ )] , while the mea- surement compatibility condition amounts to Yθk,θk′ ≡ Im [ Tr ( ρθLρθkLρθk′ )] = 0 (Ragy et al., 2016).”
A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging (2019, result): “However, it can still provide novel insights into quantum sensing and estimation impossible via the SLDCRB, for instance in simultaneous estimation of phase and loss in optical interferometry [58].”
Quantum Fisher information matrix and multiparameter estimation (2019, methodology): “After this, its generalization to mixed states was discussed in several specific scenarios [28,131–133] and rigorously proved via the Holevo bound firstly with the theory of local asymptotic normality [134] and then the direct minimization of one term in Holevo bound [135].”
Roadmap on quantum light spectroscopy (2020, background): “optimal measurements for individual parameters, a feature that the quantum Cramér–Rao approach captures only in part [64].”