  In [Berta 2014 Entanglement], uncertainty relations in the presence of
quantum memory was formulated for mutually unbiased bases using conditional
collision entropy. In this paper, we generalize their results to the mutually
unbiased measurements. Our primary result is an equality between the amount of
uncertainty for a set of measurements and the amount of entanglement of the
measured state, both of which are quantified by the conditional collision
entropy. Implications of this equality relation are discussed. We further show
that similar equality relation can be obtained for generalized symmetric
informationally complete measurements. We also derive an interesting equality
for arbitrary orthogonal basis of the space of Hermitian, traceless operators.
