Quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimation

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

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)
12 Downloads (Pure)

Abstract

We propose quantum versions of the Bell-Ziv-Zakai lower bounds for 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/N2(p-1)/(p+1), where N is the time-averaged mean photon flux. Moreover, we show that this scaling 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.

Original languageEnglish
Article number031018
Pages (from-to)1-28
Number of pages28
JournalPhysical Review X
Volume5
Issue number3
DOIs
Publication statusPublished - 18 Aug 2015

Bibliographical note

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