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?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.

 

About the Speaker: Dominic Berry is an ARC Future Fellow at the Department of Physics and Astronomy of Macquarie University. He obtained his PhD from the University of Queensland in 2002 and held positions in Macquarie University and the University of Waterloo, before joining the faculty at Macquarie in 2011. His main contributions are in the areas of quantum information and quantum optics, where he developed most efficient algorithms for simulation of physical systems and most accurate known methods to measure optical phase by using adaptive techniques. More information about his research activities can be found at www.dominicberry.org.