Quantum parameter estimation using general single-mode Gaussian states

Pinel, Olivier; Jian, Pu; Treps, Nicolas; Fabre, Claude; Braun, Daniel

doi:10.1103/physreva.88.040102

Cited by 189 publications

(214 citation statements)

References 29 publications

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“…We are now able to derive an expression of the QFI thanks to results from [28] and expressions for fidelity between Gaussian states [32]. One can also use the derivations in [33][34][35] which are applications of the results in [28] to Gaussian states. As expected, all these expressions of the QFI for Gaussian states are functions of the first and second moment of the quadrature operators.…”

Section: Derivation Of the Metrological Quantities For Gaussian mentioning

confidence: 99%

“…Note that the use of the result of [33] requires that the initial probe state is Gaussian, but this does not exclude correlation with the bath. The minimum condition is indeed that ρ 0 SB be Gaussian.…”

Section: Derivation Of the Metrological Quantities For Gaussian mentioning

confidence: 99%

“…Here we do so (Appendix A) thanks to the simple form of (4). Since in this problem of force estimation the parameter F to be estimated controls only the amplitude of the displacement in the phase space, the expression for QFI derived in [33] for Gaussian states can be simplified to…”

Section: Derivation Of the Metrological Quantities For Gaussian mentioning

confidence: 99%

“…Efforts have been made to find alternatives [28][29][30][31], but they are still hard to apply for arbitrary dynamics and states. We restrict ourselves to Gaussian states which are more easily accessible experimentally and for which [33][34][35] have derived explicit expressions of the QFI. As we will see in the following, this important assumption also guarantees that the best measurement is a quadrature measurement and that the maximum likelihood estimator is efficient implying that the quantum Cramer-Rao bound Eq.…”

Section: Derivation Of the Metrological Quantities For Gaussian mentioning

confidence: 99%

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Quantum force estimation in arbitrary non-Markovian Gaussian baths

2016

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The force estimation problem in quantum metrology with arbitrary non-Markovian Gaussian bath is considered. No assumptions are made on the bath spectrum and coupling strength with the probe. Considering the natural global unitary evolution of both bath and probe and assuming initial global Gaussian states we are able to solve the main issues of any quantum metrological problem: the best achievable precision determined by the quantum Fisher information, the best initial state and the best measurement. Studying the short time behavior and comparing to regular Markovian dynamics we observe an increase of quantum Fisher information. We emphasize that this phenomenon is due to the ability to perform measurements below the correlation time of the bath, activating non-Markovian effects. This brings huge consequences for the sequential preparation-andmeasurement scenario as the quantum Fisher information becomes unbounded when the initial probe mean energy goes to infinity, whereas its Markovian counterpart remains bounded by a constant. The long time behavior shows the complexity and potential variety of non-Markovian effects, somewhere between the exponential decay characteristic of Markovian dynamics and the sinusoidal oscillations characteristic of resonant narrow bands.

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Section: Derivation Of the Metrological Quantities For Gaussian mentioning

confidence: 99%

Section: Derivation Of the Metrological Quantities For Gaussian mentioning

confidence: 99%

Section: Derivation Of the Metrological Quantities For Gaussian mentioning

confidence: 99%

Section: Derivation Of the Metrological Quantities For Gaussian mentioning

confidence: 99%

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Quantum force estimation in arbitrary non-Markovian Gaussian baths

2016

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“…The QFI for estimation of a parameter τ using a singlemode Gaussian state σ is given in [16] and for zero displacement reduces to:…”

Section: Single-mode Reduced Covariance Matrixmentioning

confidence: 99%

Quantum estimation via parametric amplification in circuit-QED arrays

Wilkins

Sabín

2015

Phys. Rev. A

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We propose a scheme for quantum estimation by means of parametric amplification in circuit Quantum Electrodynamics. The modulation of a SQUID interrupting a superconducting waveguide transforms an initial thermal two-mode squeezed state in such a way that the new state is sensitive to the features of the parametric amplifier. We find the optimal initial parameters which maximize the Quantum Fisher Information. In order to achieve a large number of independent measurements we propose to use an array of non-interacting resonators. We show that the combination of both large QFI and large number of measurements enables, in principle, the use of this setup for Quantum Metrology applications.

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Quantum Frequency Combs

Fabre¹,

Treps²

2016

Quantum Information

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Quantum parameter estimation using general single-mode Gaussian states

Cited by 189 publications

References 29 publications

Quantum force estimation in arbitrary non-Markovian Gaussian baths

Quantum force estimation in arbitrary non-Markovian Gaussian baths

Quantum estimation via parametric amplification in circuit-QED arrays

Quantum Frequency Combs

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