  In the quest to unlock the maximum potential of quantum sensors, it is of
paramount importance to have practical measurement strategies that can estimate
incompatible parameters with best precisions possible. However, it is still not
known how to find practical measurements with optimal precisions, even for
uncorrelated measurements over probe states. Here, we give a concrete way to
find uncorrelated measurement strategies with optimal precisions. We solve this
fundamental problem by introducing a framework of conic programming that
unifies the theory of precision bounds for multiparameter estimates for
uncorrelated and correlated measurement strategies under a common umbrella.
Namely, we give precision bounds that arise from linear programs on various
cones defined on a tensor product space of matrices, including a particular
cone of separable matrices. Subsequently, our theory allows us to develop an
efficient algorithm that calculates both upper and lower bounds for the
ultimate precision bound for uncorrelated measurement strategies, where these
bounds can be tight. In particular, the uncorrelated measurement strategy that
arises from our theory saturates the upper bound to the ultimate precision
bound. Also, we show numerically that there is a strict gap between the
previous efficiently computable bounds and the ultimate precision bound.
