title: 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 Cramér-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 Cramér-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 Cramér-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.
authors.affiliation: Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117583. eletmk@nus.edu.sg
authors.forename: Mankei
authors.initials: M
authors.lastname: Tsang