Heisenberg versus standard scaling in quantum metrology with Markov generated states and monitored environment

Catana, Catalin; Guţǎ, Mădălin

doi:10.1103/physreva.90.012330

Cited by 17 publications

(15 citation statements)

References 39 publications

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“…input states. On the other hand, Markov chains with several ergodic components may fail to satisfy local asymptotic normality, and even exhibit 'Heisenberg scaling', with relevance for quantum metrology applications [7]. Our theory intersects here with that of 'thermodynamics of trajectories' and 'dynamical phase transitions' [31,32], and this connection will be further explored in a future work.…”

Section: Discussionmentioning

confidence: 53%

Equivalence Classes and Local Asymptotic Normality in System Identification for Quantum Markov Chains

Guţǎ

Kiukas

2014

Commun. Math. Phys.

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We consider the problem of identifying and estimating dynamical parameters of an ergodic quantum Markov chain, when only the stationary output is accessible for measurements. The starting point of the analysis is the fact that the knowledge of the output state completely fixes the dynamics up to an equivalence class of ?coordinate transformation? consisting of a multiplication by a phase and a unitary conjugation of the Kraus operators. Assuming that the dynamics depends on an unknown parameter, we show that the latter can be estimated at the ?standard? rate n ?1/2, and give an explicit expression of the (asymptotic) quantum Fisher information of the output, which is proportional to the Markov variance of a certain ?generator?. More generally, we show that the output is locally asymptotically normal, i.e., it can be approximated by a simple quantum Gaussian model consisting of a coherent state whose mean is related to the unknown parameter. As a consistency check, we prove that a parameter related to the ?coordinate transformation? unitaries has zero quantum Fisher informationPeer reviewe

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Section: Discussionmentioning

confidence: 53%

Equivalence Classes and Local Asymptotic Normality in System Identification for Quantum Markov Chains

Guţǎ

Kiukas

2014

Commun. Math. Phys.

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“…One can then define an effective QFI, which poses the ultimate bounds for these kinds of estimation strategies [39,48,51], and that depends both on the specific unravelling and on the monitoring efficiencies η j :…”

Section: Quantum Estimation Via Timecontinuous Measurementsmentioning

confidence: 99%

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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“…Clearly this bound can be readily applied to the timecontinuous case discussed in the main text, where the vector of outcomes y T corresponds to a measured homodyne photocurrent, and where the conditional state We should also remark that a bound of this kind has already been considered in [39], in a similar physical situation where n probes, that may be prepared in a quantum correlated initial state, are coupled to n independent environments and one performs sequentially n measurement on the respective environments and a final measurement on the conditional state of the probes.…”

Section: Appendix A: Classical and Quantum Cramér-rao Bounds For Sequmentioning

confidence: 99%

“…The goal is to recover the information on the parameter leaking into the environment and simultaneously to exploit the back action of the measurement to drive the system * francesco.albarelli@unimi.it † matteo.rossi@unimi.it ‡ matteo.paris@fisica.unimi.it § marco.genoni@fisica.unimi.it into more sensitive conditional states [25][26][27][28][29][30][31][32][33][34]. This approach has received much attention recently [35][36][37][38][39][40][41][42] also in the context of quantum magnetometry [43][44][45][46][47][48].…”

Section: Introductionmentioning

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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Heisenberg versus standard scaling in quantum metrology with Markov generated states and monitored environment

Cited by 17 publications

References 39 publications

Equivalence Classes and Local Asymptotic Normality in System Identification for Quantum Markov Chains

Equivalence Classes and Local Asymptotic Normality in System Identification for Quantum Markov Chains

Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment

Ultimate limits for quantum magnetometry via time-continuous measurements

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