  Quantifying quantum mechanical uncertainty is vital for the increasing number
of experiments that reach the uncertainty limited regime. We present a method
for computing tight variance uncertainty relations, i.e., the optimal
state-independent lower bound for the sum of the variances for any set of two
or more measurements. The bounds come with a guaranteed error estimate, so
results of pre-assigned accuracy can be obtained straightforwardly. Our method
also works for POVM measurements. Therefore, it can be used for detecting
entanglement in noisy environments, even in cases where conventional spin
squeezing criteria fail because of detector noise.
