Cramér-Rao bound for time-continuous measurements in linear Gaussian quantum systems

Genoni, Marco G.

doi:10.1103/physreva.95.012116

Cited by 23 publications

(22 citation statements)

References 49 publications

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“…A method for the calculation of F[p traj ] has been firstly proposed in [41] for generic quantum states, and then in [44] for continuous-variable Gaussian states. In Sec.…”

Section: Quantum Estimation Via Timecontinuous Measurementsmentioning

confidence: 99%

“…Time-continuous measurements have been often studied as a tool for quantum parameter/state estimation [29][30][31][32][33][34][35][36], with a particular focus on classical time-dependent signals [37][38][39]. More recently, methods to calculate classical and quantum Cramér-Rao bounds for parameter estimation via time-continuous monitoring have been proposed [40][41][42][43][44], and put into action [45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

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Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment

Albarelli

Rossi

Tamascelli

et al. 2018

Quantum

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We study quantum frequency estimation for N qubits subject to independent Markovian noise via strategies based on time-continuous monitoring of the environment. Both physical intuition and the extended convexity of the quantum Fisher information (QFI) suggest that these strategies are more effective than the standard ones based on the measurement of the unconditional state after the noisy evolution. Here we focus on initial GHZ states subject to parallel or transverse noise. For parallel, i.e., dephasing noise, we show that perfectly efficient timecontinuous photodetection allows us to recover the unitary (noiseless) QFI, and hence obtain Heisenberg scaling for every value of the monitoring time. For finite detection efficiency, one falls back to noisy standard quantum limit scaling, but with a constant enhancement due to an effective reduced dephasing. In the transverse noise case, Heisenberg scaling is recovered for perfectly efficient detectors, and we find that both homodyne and photodetection-based strategies are optimal. For finite detector efficiency, our numerical simulations show that, as expected, an enhancement can be observed, but we cannot give any conclusive statement regarding the scaling. We finally describe in detail the stable and compact numerical algorithm that we have developed in order to evaluate the precision of such time-continuous estimation strategies, and that may find application in other quantum metrology schemes.Accepted in Quantum 2018-11-29, click title to verify arXiv:1803.05891v3 [quant-ph]

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“…A method for the calculation of F[p traj ] has been firstly proposed in [41] for generic quantum states, and then in [44] for continuous-variable Gaussian states. In Sec.…”

Section: Quantum Estimation Via Timecontinuous Measurementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment

Albarelli

Rossi

Tamascelli

et al. 2018

Quantum

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“…The ultimate limit on the precision of this estimate is quantified by the FI F[p(y t )]. Given the Gaussian nature and the simple dynamics of the problem we can compute it analytically in closed form, by applying the results of [58]. As we describe in more detail in B, one obtains the formula…”

Section: A Analytical Fi Corresponding To the Time-continuous Photocmentioning

confidence: 99%

Ultimate limits for quantum magnetometry via time-continuous measurements

et al. 2017

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We address the estimation of the magnetic field B acting on an ensemble of atoms with total spin J subjected to collective transverse noise. By preparing an initial spin coherent state, for any measurement performed after the evolution, the mean-square error of the estimate is known to scale as 1/J, i.e. no quantum enhancement is obtained. Here, we consider the possibility of continuously monitoring the atomic environment, and conclusively show that strategies based on time-continuous non-demolition measurements followed by a final strong measurement may achieve Heisenberg-limited scaling 1/J 2 and also a monitoring-enhanced scaling in terms of the interrogation time. We also find that time-continuous schemes are robust against detection losses, as we prove that the quantum enhancement can be recovered also for finite measurement efficiency. Finally, we analytically prove the optimality of our strategy.

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“…Continuous measurements have been proposed for different quantum estimation problems, e.g. for magnetometry [10][11][12][13][14], phase tracking [15,16], waveform estimation [17], state estimation and generic dynamical parameters [18][19][20][21][22][23][24][25][26][27][28]. In particular, in our previous paper [29] we have shown the usefulness of continuous monitoring to counteract the effect of noise in frequency estimation.…”

Section: Introductionmentioning

confidence: 99%

Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels

Albarelli

Rossi

Genoni

2020

Int. J. Quantum Inform.

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We discuss the problem of estimating a frequency via N -qubit probes undergoing independent dephasing channels that can be continuously monitored via homodyne or photo-detection. We derive the corresponding analytical solutions for the conditional states, for generic initial states and for arbitrary efficiency of the continuous monitoring. For the detection strategies considered, we show that: i) in the case of perfect continuous detection, the quantum Fisher information (QFI) of the conditional states is equal to the one obtained in the noiseless dynamics; ii) for smaller detection efficiencies, the QFI of the conditional state is equal to the QFI of a state undergoing the (unconditional) dephasing dynamics, but with an effectively reduced noise parameter.

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Cramér-Rao bound for time-continuous measurements in linear Gaussian quantum systems

Cited by 23 publications

References 49 publications

Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment

Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment

Ultimate limits for quantum magnetometry via time-continuous measurements

Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels

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