  This paper explores the effect of three-dimensional rotations on two-qubit
Bell states and proposes a Bayesian method for the estimation of the parameters
of the rotation. We use a particle filter to estimate the parameters of the
rotation from a sequence of Bell state measurements and we demonstrate that the
resultant improvement over the optimal single qubit case approaches the
$\sqrt{2}$ factor that is consistent with the Heisenberg limit. We also
demonstrate how the accuracy of the estimation method is a function of the
purity of mixed states.
