Alternative measures of uncertainty in quantum metrology: Contradictions and limits

We propose quantum versions of the Bell-Ziv-Zakai lower bounds on the error in multiparameter estimation. As an application we consider measurement of a time-varying optical phase signal with stationary Gaussian prior statistics and a power law spectrum ∼ 1/|ω| p , with p > 1. With no other assumptions, we show that the mean-square error has a lower bound scaling as 1/N 2(p−1)/(p+1) , where N is the time-averaged mean photon flux. Moreover, we show that this accuracy is achievable by sampling and interpolation, for any p > 1. This bound is thus a rigorous generalization of the Heisenberg limit, for measurement of a single unknown optical phase, to a stochastically varying optical phase.

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“…(2. 19). It can be further simplified if F (x, x+vτ ) does not depend on x and the prior P X (x) is a multivariate Gaussian distribution.…”

Section: B Quantum Estimationmentioning

confidence: 99%

Quantum Bell-Ziv-Zakai Bounds and Heisenberg Limits for Waveform Estimation

et al. 2015

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“…Here, the sub-Heisenberg scaling manifests in terms of the average photon number N and might mislead to conclude that it violates the fundamental Heisenberg limit. More details on that can be found in the relevant debates, which have been devoted over the last decade [18][19][20][21][22][23][24][25], followed by the conclusive proofs [22,[26][27][28][29][30][31][32][33]. The latter showed that the overall scaling, while including the amount of resources required for obtaining a priori probability distribution of the parameter and the number of measurements required to achieve the asymptotic bound, is still Heisenberg scaling-limited.…”

Section: Introductionmentioning

confidence: 99%

Using states with a large photon number variance to increase quantum Fisher information in single-mode phase estimation

Lee

Jeong

et al. 2019

J. Phys. Commun.

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When estimating the phase of a single mode, the quantum Fisher information for a pure probe state is proportional to the photon number variance of the probe state. In this work, we point out particular states that offer photon number distributions exhibiting a large variance, which would help to improve the local estimation precision. These theoretical examples are expected to stimulate the community to put more attention to those states that we found, and to work towards their experimental realization and usage in quantum metrology.

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“…The actual meaning of the strong Heisenberg limit has been much debated [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. However, the weak Heisenberg limit has not so extensively examined [5,23,30], although it has a more deep practical meaning as discussed above.…”

Section: Introductionmentioning

confidence: 99%