  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 $\sim 1/|\omega|^p$, with $p>1$. With no other
assumptions, we show that the mean-square error has a lower bound scaling as
$1/{\cal N}^{2(p-1)/(p+1)}$, where ${\cal N}$ 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.
