Multiparameter Heisenberg limit
arXiv:1403.4080
Abstract
Using a quantum version of the Bell-Ziv-Zakai bound, I derive a Heisenberg limit to multiparameter estimation for any Gaussian prior probability density. The mean-square error lower bound is shown to have a universal quadratic scaling with respect to a quantum resource, such as the average photon number in the case of optical phase estimation, suitably weighted by the prior covariance matrix.
First draft. Note that this result has since been extended, merged into arXiv:1409.7877, and published in Physical Review X