On the discontinuity of the quantum Fisher information for quantum statistical models with parameter dependent rank

The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such multiparameter estimation can be achieved depends on understanding the many subtleties that come into play: establishing solid foundations is key to delivering future technology for this task. In this article we discuss the state of the art of quantum multiparameter estimation, with a particular emphasis on its theoretical tools, on application to imaging problems, and on the possible avenues towards the next developments.

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“…The case of variable rank models is somewhat pathological, being akin to the topic non-regular models in classical statistics[74].…”

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confidence: 99%

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

et al. 2020

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“…II C. Thus, for this state the QFI and FI are provided in Eqs. (49) and (50), respectively (see also Fig. 13).…”

Section: Star Graphmentioning

confidence: 84%

“…This establishes the ultimate lower bound of the precision in estimating a parameter λ encoded in a quantum state. Note that the QCR inequality is valid for regular quantum statistical models, i.e., families of quantum states made of density matrices with constant rank (i.e., the rank does not depend on the parameter) and leading to nonsingular QFI [48][49][50].…”

Section: Characterizationmentioning

confidence: 99%

Continuous-time quantum walks in the presence of a quadratic perturbation

et al. 2020

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We address the properties of continuous-time quantum walks with Hamiltonians of the form H = L + λL 2 , with L the Laplacian matrix of the underlying graph and the perturbation λL 2 motivated by its potential use to introduce next-nearest-neighbor hopping. We consider cycle, complete, and star graphs as paradigmatic models with low and high connectivity and/or symmetry. First, we investigate the dynamics of an initially localized walker. Then we devote attention to estimating the perturbation parameter λ using only a snapshot of the walker dynamics. Our analysis shows that a walker on a cycle graph spreads ballistically independently of the perturbation, whereas on complete and star graphs one observes perturbation-dependent revivals and strong localization phenomena. Concerning the estimation of the perturbation, we determine the walker preparations and the simple graphs that maximize the quantum Fisher information. We also assess the performance of position measurement, which turns out to be optimal, or nearly optimal, in several situations of interest. Besides fundamental interest, our study may find applications in designing enhanced algorithms on graphs.

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“…Discontinuous behavior of the Fisher information was recently studied in Refs. [38,39] but a possible relation to these observations remains open for future investigations. More generally, this shows that the sensitivity of phase estimation experiments based on the widely used method of moments can depend strongly on the precise implementation of the measurement observable.…”

Section: Discussionmentioning

confidence: 94%

Enhancement of the metrological sensitivity limit through knowledge of the average energy

Gessner

2019

Phys. Rev. A

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We consider the problem of quantum phase estimation with access to arbitrary measurements in a single suboptimal basis. The achievable sensitivity limit in this case is determined by the classical Cramér-Rao bound with respect to the fixed basis. Here we show that the sensitivity can be enhanced beyond this limit if knowledge about the energy expectation value is available. The combined information is shown to be equivalent to a direct measurement of an optimal linear combination of the basis projectors and the phase-imprinting Hamiltonian. Application to an atomic clock with oversqueezed spin states yields a sensitivity gain that scales linearly with the number of atoms. Our analysis further reveals that small modifications of the observable can have a strong impact on the sensitivity.

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On the discontinuity of the quantum Fisher information for quantum statistical models with parameter dependent rank

Cited by 48 publications

References 42 publications

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

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

Continuous-time quantum walks in the presence of a quadratic perturbation

Enhancement of the metrological sensitivity limit through knowledge of the average energy

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