Loss-induced limits to phase measurement precision with maximally entangled states

Rubin, Mark A.; Kaushik, Sumanth

doi:10.1103/physreva.75.053805

Cited by 87 publications

(70 citation statements)

References 61 publications

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“…Such extreme sensitivity to losses implies that this state cannot be used in any practical situation [68,98,99]. Is it then really possible to outperform classical strategies in practical phase sensing [100]?…”

Section: Quantum Metrology With Noisementioning

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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Section: Quantum Metrology With Noisementioning

confidence: 99%

Advances in quantum metrology

2011

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“…We first consider the role of photon loss by introducing a fictitious beam splitter in one of two arms after the phase accumulation [32][33][34][35][36][37]. Only the absorption of photons that carries the phase information is important, so the phase-dependent state can be rewritten as |ψ(φ)…”

Section: Binary-outcome Detections Under the Phase Diffusionmentioning

confidence: 99%

Quantum interferometry with binary-outcome measurements in the presence of phase diffusion

2014

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Optimal measurement scheme with an efficient data processing is important in quantum-enhanced interferometry. Here we prove that for a general binary-outcome measurement, the simplest data processing based on inverting the average signal can saturate the Cramér-Rao bound. This idea is illustrated by binary-outcome homodyne detection, even-odd photon counting (i.e., parity detection), and zero-nonzero photon counting that have achieved super-resolved interferometric fringe and shot-noise limited sensitivity in coherent-light MachZehnder interferometer. The roles of phase diffusion are investigated in these binary-outcome measurements. We find that the diffusion degrades the fringe resolution and the achievable phase sensitivity. Our analytical results confirm that the zero-nonzero counting can produce a slightly better sensitivity than that of the parity detection, as demonstrated in a recent experiment.

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“…Environmentally induced decoherence, however, significantly affects the performance of entanglement based quantum strategies [12][13][14][15][16][17][18][19][20][21] with photon loss being its most relevant source in optical implementations. The need to balance the phase sensitivity and robustness against losses results in states performing better than SQL yet falling short of HL [18,19].…”

Section: Introductionmentioning

confidence: 99%