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Quantum Foundations

The quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimation

arXiv

Authors: Dominic W. Berry, Mankei Tsang, Michael J. W. Hall, Howard M. Wiseman

Year

2014

Paper ID

47277

Status

Preprint

Abstract Read

~2 min

Abstract Words

110

Citations

N/A

Abstract

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 sim 1/|ω|^p, with p>1. With no other assumptions, we show that the mean-square error has a lower bound scaling as 1/{cal N}^2(p-1)/(p+1), where {cal 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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We propose quantum versions of the Bell-Ziv-Zakai lower bounds on the error in multiparameter estimation.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1409.7877 [2] arXiv https://arxiv.org/abs/1409.7877 [3] Publisher https://arxiv.org/abs/1409.7877

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