Quantum metrology beyond the quantum Cramér-Rao theorem

Seveso, Luigi; Rossi, Matteo A. C.; Paris, Matteo G. A.

doi:10.1103/physreva.95.012111

Cited by 38 publications

(28 citation statements)

References 27 publications

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“…the CRB saturates the QCRB. In order to be precise, we note that the last statement is valid for quantum parameter-independent measurements, otherwise one should refer to more general bounds on the FI [53]. On top of this, another significant quantity in assessing the performances of an estimator, is the signal-tonoise ratio (SNR), which is defined as SNR ≡ λ 2 /Var λ .…”

Section: B Local Qet For Gaussian Statesmentioning

confidence: 99%

Continuous-variable quantum probes for structured environments

2018

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We address parameter estimation for complex/structured systems and suggest an effective estimation scheme based on continuous-variables quantum probes. In particular, we investigate the use of a single bosonic mode as a probe for Ohmic reservoirs, and obtain the ultimate quantum limits to the precise estimation of their cutoff frequency. We assume the probe prepared in a Gaussian state and determine the optimal working regime, i.e. the conditions for the maximization of the quantum Fisher information in terms of the initial preparation, the reservoir temperature and the interaction time. Upon investigating the Fisher information of feasible measurements we arrive at a remarkable simple result: homodyne detection of canonical variables allows one to achieve the ultimate quantum limit to precision under suitable, mild, conditions. Finally, upon exploiting a perturbative approach, we find the invariant sweet spots of the (tunable) characteristic frequency of the probe, able to drive the probe towards the optimal working regime.

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Section: B Local Qet For Gaussian Statesmentioning

confidence: 99%

Continuous-variable quantum probes for structured environments

2018

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“…B. Cylinder in a radial magnetic field In Section 2.2.2 we have written the Schröedinger equation for a particle of mass M , and electric charge Q, moving on the surface of a cylinder with radius λ immersed in a magnetic field (22). Let us now focus on the specific case where the magnetic field has only a radial component B 1 , whereas the axial component is vanishing B 0 = 0.…”

Section: A Sphere In a Magnetic Fieldmentioning

confidence: 99%

“…In order to quantify the available information about the curvature, that may be extracted by means of a measurement on the particle, we employ ideas and tools from quantum parameter estimation (QPE) theory [17][18][19][20][21][22]. QPE generalizes to the quantum case the problem of point estimation arising in classical statistics.…”

Section: Introductionmentioning

confidence: 99%

Quantum Sensing of Curvature

2019

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We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and the manifold is a surface embedded in the three-dimensional Euclidean space. We exploit ideas and tools from quantum estimation theory to quantify the amount of information encoded into a state of the particle, and to seek for optimal probing schemes, able to actually extract this information. Explicit results are found for a free probing particle and in the presence of a magnetic field. We also address precision achievable by position measurement, and show that it provides a nearly optimal detection scheme, at least to estimate the radius of a sphere or a cylinder.

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“…Assuming that there is the (multidimensional) Fourier transform of Q a ( )(as in the case of the Husimi function equation (20)), one can show that there is the inverse transform to equation (25). Let us write the Fourier transform using the complex variables:…”

Section: Appendix Amentioning

confidence: 99%

Quantum state and mode profile tomography by the overlap

et al. 2018

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Any measurement scheme involving interference of quantum states of the electromagnetic field necessarily mixes information about the spatiotemporal structure of these fields and quantum states in the recorded data. We show that in this case, a trade-off is possible between extracting information about the quantum states and the structure of the underlying fields, with the modal overlap being either a goal or a convenient tool of the reconstruction. We show that varying quantum states in a controlled way allows one to infer temporal profiles of modes. Vice versa, for the known quantum state of the probe and controlled variable overlap, one can infer the quantum state of the signal. We demonstrate this trade-offby performing an experiment using the simplest on-off detection in an unbalanced weak homodyning scheme. For the single-mode case, we demonstrate experimentally inference of the overlap and a few-photon signal state. Moreover, we show theoretically that the same single-detector scheme is sufficient even for arbitrary multi-mode fields.about the underlying mode structure. Indeed, given a known quantum state occupying an unknown mode, this method can be used to infer the overlap, and, thus, to identify the shape of this mode. In this sense, it may be considered as a diagnostic tool for existing tomographic reconstructions schemes, where identifying the modes is crucial to measuring the whole state [10]. Several techniques have been shown to shape temporal mode profiles [11][12][13][14][15][16][17][18][30][31][32][33][34][35] and the method to infer a modal temporal profile has a considerable practical value.We demonstrate these techniques experimentally using heralded single and two-photon states in welldefined modes and coherent probe field. The suggested tomographic scheme is resource efficient, requiring a single on-off detector. We show that for an arbitrary known signal with a diagonal density matrix, the overlap modulus can be found from just one measurement. This can be an important advantage over, for example, standard quantum homodyne tomography with a strong probe. For instance, for single-photon strong-probe homodyning, involved algorithms for fitting the temporal profile are needed for reconstruction [19]. Moreover, by weak-probe homodyning it is possible to infer the overlap even for the unknown quantum state of the signal [9]. For that, measurements should be done for the set of different detection efficiencies, in addition to the variation in a controlled way of the quantum state of the probe. Note that the variable overlap can be also used for the reconstruction with the thermal probe. Finally, theoretically, we extend the scheme to cover the more general case where the signal occupies multiple modes.The outline of the paper is as follows. In section 2 we introduce the concept of the overlap and temporal profile, describe the scheme and discuss the role of the overlap for the simplest single-mode case. In section 3 we describe the measurement set-up and experimental results for the signal stat...

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Quantum metrology beyond the quantum Cramér-Rao theorem

Cited by 38 publications

References 27 publications

Continuous-variable quantum probes for structured environments

Continuous-variable quantum probes for structured environments

Quantum Sensing of Curvature

Quantum state and mode profile tomography by the overlap

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