Interferometric detection of optical phase shifts at the Heisenberg limit

Holland, Murray; Burnett, K.

doi:10.1103/physrevlett.71.1355

Cited by 821 publications

(862 citation statements)

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“…The degeneracy of the spectrum of the the Hamiltonian can be treated using the technique of [6] and, in this way, the problem is reduced to a nondegenerate one with spectrum Z for the phase-shift operator. The δφ ∝ N −1 scaling in interferometry has also been found for specific classes of input states such as optimized squeezed states [10] and number states [11]. Our analysis confirms such an unsurpassable bound, and provides the optimal states which, compared to states of [10,11], show a largely reduced multiplicative constant.…”

Section: Discussionsupporting

confidence: 70%

Optimal quantum estimation of the coupling between two bosonic modes

D’Ariano

Paris

Perinotti

2001

J. Opt. B: Quantum Semiclass. Opt.

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Section: Discussionsupporting

confidence: 70%

Optimal quantum estimation of the coupling between two bosonic modes

D’Ariano

Paris

Perinotti

2001

J. Opt. B: Quantum Semiclass. Opt.

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“…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.…”

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confidence: 99%

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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“…This includes approaches to loss-tolerant quantum metrology, such as Holland and Burnett states. [24][25][26][27] To perform experiments with n photons, post-selection is commonly used to ignore components of fewer photons (o n), whereas terms associated with higher-photon number (4n) are treated as noise. This is particularly problematic for quantum metrology, where all photons passing through the sample need to be accounted for, and unwanted photon-number components are detrimental to measurement precision.…”

Section: Introductionmentioning

confidence: 99%

Towards practical quantum metrology with photon counting

et al. 2016

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Quantum metrology aims to realise new sensors operating at the ultimate limit of precision measurement. However, optical loss, the complexity of proposed metrology schemes and interferometric instability each prevent the realisation of practical quantumenhanced sensors. To obtain a quantum advantage in interferometry using these capabilities, new schemes are required that tolerate realistic device loss and sample absorption. We show that loss-tolerant quantum metrology is achievable with photoncounting measurements of the generalised multi-photon singlet state, which is readily generated from spontaneous parametric downconversion without any further state engineering. The power of this scheme comes from coherent superpositions, which give rise to rapidly oscillating interference fringes that persist in realistic levels of loss. We have demonstrated the key enabling principles through the four-photon coincidence detection of outcomes that are dominated by the four-photon singlet term of the four-mode downconversion state. Combining state-of-the-art quantum photonics will enable a quantum advantage to be achieved without using post-selection and without any further changes to the approach studied here.

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Interferometric detection of optical phase shifts at the Heisenberg limit

Cited by 821 publications

References 10 publications

Optimal quantum estimation of the coupling between two bosonic modes

Optimal quantum estimation of the coupling between two bosonic modes

Advances in quantum metrology

Towards practical quantum metrology with photon counting

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