Ziv-Zakai Error Bounds for Quantum Parameter Estimation
Abstract
I propose quantum versions of the Ziv-Zakai bounds as alternatives to the widely used quantum Cram\'er-Rao bounds for quantum parameter estimation. From a simple form of the proposed bounds, I derive both a "Heisenberg" error limit that scales with the average energy and a limit similar to the quantum Cram\'er-Rao bound that scales with the energy variance. These results are further illustrated by applying the bound to a few examples of optical phase estimation, which show that a quantum Ziv-Zakai bound can be much higher and thus tighter than a quantum Cram\'er-Rao bound for states with highly non-Gaussian photon-number statistics in certain regimes and also stay close to the latter where the latter is expected to be tight.
Cite
@article{arxiv.1111.3568,
title = {Ziv-Zakai Error Bounds for Quantum Parameter Estimation},
author = {Mankei Tsang},
journal= {arXiv preprint arXiv:1111.3568},
year = {2012}
}
Comments
v1: preliminary result, 3 pages; v2: major update, 4 pages + supplementary calculations, v3: another major update, added proof of "Heisenberg" limit, v4: accepted by PRL