Optimal Quantum Phase Estimation

Dorner, U.; Demkowicz-Dobrzański, Rafał; Smith, Brian J.; Lundeen, Jeff S.; Wasilewski, Wojciech; Banaszek, Konrad; Walmsley, Ian A.

doi:10.1103/physrevlett.102.040403

Cited by 446 publications

(521 citation statements)

References 23 publications

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“…A post-selected proof of principle experiment that employs some of these optimal states was recently performed [66]. Note that, for very low values of loss, NOON states retain their optimality [104,106], and can be approximated by states that are easy to generate [67,68]. Also, a very simple proposal based on parametric downconversion which can be realized without post-selection was proposed in [72]: it can achieve the Heisenberg bound for low loss and degrades gracefully with noise.…”

Section: Quantum Metrology With Noisementioning

confidence: 99%

“…While this means that quantum approaches are useful in highly controlled environments [102] (such as for gravitational wave detection [1]), they only allow for very small enhancements in free-space target acquisition [102]. Nonetheless, the shot noise can be beaten [103] and the optimal states to do so in the presence of loss have been calculated numerically using various optimization techniques for fixed number of input photons [104,105] and for photon-number detection [106]. A post-selected proof of principle experiment that employs some of these optimal states was recently performed [66].…”

Section: Quantum Metrology With Noisementioning

confidence: 99%

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Advances in quantum metrology

2011

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In classical estimation theory, the central limit theorem implies that the statistical error in a measurement outcome can be reduced by an amount proportional to n −1/2 by repeating the measures n times and then averaging. Using quantum effects, such as entanglement, it is often possible to do better, decreasing the error by an amount proportional to n −1 . Quantum metrology is the study of those quantum techniques that allow one to gain advantages over purely classical approaches.In this review, we analyze some of the most promising recent developments in this research field. Specifically, we deal with the developments of the theory and point out some of the new experiments. Then we look at one of the main new trends of the field, the analysis of how the theory must take into account the presence of noise and experimental imperfections.Any measurement consists in three parts: the preparation of a probe, its interaction with the system to be measured, and the probe readout. This process is often plagued by statistical or systematic errors. The source of the former can be accidental (e.g. deriving from an insufficient control of the probes or of the measured system) or fundamental (e.g. deriving from the Heisenberg uncertainty relations). Whatever their origin, we can reduce their effect by repeating the measurement and averaging the resulting outcomes. This is a consequence of the central-limit theorem: given a large number n of independent measurement results (each having a standard deviation ∆σ), their average will converge to a Gaussian distribution with standard deviation ∆σ/ √ n, so that the error scales as n −1/2 . In quantum mechanics this behavior is referred to as "standard quantum limit" (SQL) and is associated with procedures which do not fully exploit the quantum nature of the system under investigation 1 . Notably it is possible to do better when one employs quantum effects, such as entanglement among the probing devices employed for the measurements, e.g. see Refs. [1][2][3][4][5][6]. Consequently, the SQL is not a fundamental quantum mechanical bound as it can be surpassed by using "non-classical" strategies. Nonetheless, through Heisenberg-like uncertainty relations, quantum mechanics still sets ultimate limits in precision which are typically referred to as "Heisenberg bounds". In Fig. 1 we present a simple example which may be useful to un-1 In quantum optics, the n −1/2 scaling is also indicated as "shot noise", since it is connected to the discrete nature of the radiation that can be heard as "shots" in a photon counter operating in Geiger mode.derstand the quantum enhancement. Part of the emerging field of quantum technology [7], quantum metrology studies these bounds and the (quantum) strategies which allows us to attain them. More generally it deals with measurement and discrimination procedures that receive some kind of enhancement (in precision, efficiency, simplicity of implementation, etc.) through the use of quantum effects. This paper aims to review some of the most recent developmen...

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Section: Quantum Metrology With Noisementioning

confidence: 99%

Section: Quantum Metrology With Noisementioning

confidence: 99%

Advances in quantum metrology

2011

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“…On the other hand , however, interaction between a system and an environment is unavoidable in reality, and the quantum decoherence induced by such interactions may decrease the QFI and destroy the quantum entanglement in the probe system exploited to improve the precision. In this regard, It has been shown that the interaction between a system and an environment usually makes the measurements noisy, which in turn degrades the estimation precision [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic shielding in quantum metrology

Jin

2015

Phys. Rev. A

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The dynamics of the quantum Fisher information of the parameters of the initial atomic state and atomic transition frequency is studied, in the framework of open quantum systems, for a static polarizable two-level atom coupled in the multipolar scheme to a bath of fluctuating vacuum electromagnetic fields without and with the presence of a reflecting boundary. Our results show that in the case without a boundary, the electromagnetic vacuum fluctuations always cause the quantum Fisher information of the initial parameters and thus the precision limit of parameter estimation to decrease. Remarkably, however, with the presence of a boundary, the quantum Fisher information becomes position and atomic polarization dependent, and as a result, it may be enhanced as compared to that in the case without a boundary and may even be shielded from the influence of the vacuum fluctuations in certain circumstances as if it were a closed system.

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“…Current research on linear interferometers is directed at the search for optimal input states and output measurements [2][3][4][5][6][7][8][9][10][11][12], adaptive phase measurement schemes [13][14][15][16], and the influence of particle losses [17][18][19]. Several proof-ofprinciple experiments reaching a sub shot-noise sensitivity have been performed, for a fixed number of particles with photons [20][21][22][23][24] and ions [25], while squeezed states for interferometry with a non-fixed number of particles have been prepared with Bose-Einstein-condensates [26][27][28][29][30], atoms at room temperature [31] and light [32,33].…”

Section: Introductionmentioning

confidence: 99%

Not all pure entangled states are useful for sub-shot-noise interferometry

2010

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We investigate the connection between the shot-noise limit in linear interferometers and particle entanglement. In particular, we ask whether or not sub shot-noise sensitivity can be reached with all pure entangled input states of N particles if they can be optimized with local operations. Results on the optimal local transformations allow us to show that for N = 2 all pure entangled states can be made useful for sub shot-noise interferometry while for N > 2 this is not the case. We completely classify the useful entangled states available in a bosonic two-mode interferometer. We apply our results to several states, in particular to multi-particle singlet states and to cluster states. The latter turn out to be practically useless for sub shot-noise interferometry. Our results are based on the Cramer-Rao bound and the Fisher information.

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Optimal Quantum Phase Estimation

Cited by 446 publications

References 23 publications

Advances in quantum metrology

Advances in quantum metrology

Electromagnetic shielding in quantum metrology

Not all pure entangled states are useful for sub-shot-noise interferometry

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