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

Albarelli, Francesco; Barbieri, Marco; Genoni, Marco G.; Gianani, Ilaria

doi:10.1016/j.physleta.2020.126311

Cited by 155 publications

(162 citation statements)

References 205 publications

(285 reference statements)

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“…Rather, we present the minimal background needed for the presentation of our results in a self contained manner. For a proper and up-to-date introduction to the field we refer to several very recent reviews which cover the state-of-the-art theoretical results as well as applications to concrete tasks [42][43][44][45].…”

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confidence: 99%

Uncertainty and trade-offs in quantum multiparameter estimation

Kull¹,

Guérin²,

Verstraete³

2020

J. Phys. A: Math. Theor.

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Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between complementary pieces of information about the system. In Quantum multiparameter estimation, such trade-offs occur for the precision achievable for different parameters characterizing a density matrix: an uncertainty relation emerges between the achievable variances of the different estimators. This is in contrast to classical multiparameter estimation, where simultaneous optimal precision is attainable in the asymptotic limit. We study trade-off relations that follow from known tight bounds in quantum multiparameter estimation. We compute trade-off curves and surfaces from Cramér-Rao type bounds which provide a compelling graphical representation of the information encoded in such bounds, and argue that bounds on simultaneously achievable precision in quantum multiparameter estimation should be regarded as measurement uncertainty relations. From the state-dependent bounds on the expected cost in parameter estimation, we derive a state independent uncertainty relation between the parameters of a qubit system.Ever since its first formulation, the uncertainty principle has seen many refinements and clarifications. As quantum theory developed, its state-of-the-art concepts and mathematical tools were used to formulate in precise terms the ideas which were put forward in Heisenberg's 1927 paper [1]. As a result, our current understanding of the uncertainties inherent in quantum mechanics is spelled out in a collection of theorems pertaining to well defined operational tasks.Soon after Heisenberg's paper, rigorous proofs of his uncertainty relations were formulated [2][3][4]. Those are usually referred to as preparation uncertainty relations. Most well known is the relation due to Weyl and Robertson arXiv:2002.05961v1 [quant-ph]

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confidence: 99%

Uncertainty and trade-offs in quantum multiparameter estimation

Kull¹,

Guérin²,

Verstraete³

2020

J. Phys. A: Math. Theor.

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“…Even the study of photonic realization of probes states can be improved by GA algorithms [47,50,51], giving rise to accessible and robust-to-noise states for metrology tasks. Then, a natural generalization of this approach is to apply GA optimization for offline protocols in multiparameter quantum metrology problems [17,[77][78][79], with particular attention to the limited data regime [80]. While online adaptive Bayesian techniques for multiphase estimation were demonstrated [81], offline solutions have still to be explored and GA promises to be a useful tool for this task.…”

Section: Discussionmentioning

confidence: 99%

Adaptive phase estimation through a genetic algorithm

Rambhatla

D'Aurelio

Valeri

et al. 2020

Phys. Rev. Research

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Quantum metrology is one of the most relevant applications of quantum information theory to quantum technologies. Here, quantum probes are exploited to overcome classical bounds in the estimation of unknown parameters. In this context, phase estimation, where the unknown parameter is a phase shift between two modes of a quantum system, is a fundamental problem. In practical and realistic applications, it is necessary to devise methods to optimally estimate an unknown phase shift by using a limited number of probes. Here we introduce and experimentally demonstrate a machine learning-based approach for the adaptive estimation of a phase shift in a Mach-Zehnder interferometer, tailored for optimal performances with limited resources. The employed technique is a genetic algorithm used to devise the optimal feedback phases employed during the estimation in an offline fashion. The results show the capability to retrieve the true value of the phase by using few photons, and to reach the sensitivity bounds in such small probe regime. We finally investigate the robustness of the protocol with respect to common experimental errors, showing that the protocol can be adapted to a noisy scenario. Such approach promises to be a useful tool for more complex and general tasks where optimization of feedback parameters is required.

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“…Furthermore, the sensitivity limit defined by the inverse of the quantum Fisher information matrix, namely, the multiparameter quantum Cramér–Rao bound 35 , is, in general, not saturable 36 , 37 . Alternative approaches based on the Holevo bound are in principle asymptotically saturable but require, in general, complex measurements on multiple copies of the state 38 – 42 .…”

Section: Introductionmentioning

confidence: 99%

Multiparameter squeezing for optimal quantum enhancements in sensor networks

2020

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Squeezing currently represents the leading strategy for quantum enhanced precision measurements of a single parameter in a variety of continuous-and discrete-variable settings and technological applications. However, many important physical problems including imaging and field sensing require the simultaneous measurement of multiple unknown parameters. The development of multiparameter quantum metrology is yet hindered by the intrinsic difficulty in finding saturable sensitivity bounds and feasible estimation strategies. Here, we derive the general operational concept of multiparameter squeezing, identifying metrologically useful states and optimal estimation strategies. When applied to spin-or continuousvariable systems, our results generalize widely-used spin-or quadrature-squeezing parameters. Multiparameter squeezing provides a practical and versatile concept that paves the way to the development of quantum-enhanced estimation of multiple phases, gradients, and fields, and for the efficient characterization of multimode quantum states in atomic and optical sensor networks.

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

Cited by 155 publications

References 205 publications

Uncertainty and trade-offs in quantum multiparameter estimation

Uncertainty and trade-offs in quantum multiparameter estimation

Adaptive phase estimation through a genetic algorithm

Multiparameter squeezing for optimal quantum enhancements in sensor networks

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