Bayesian Estimation for Bell State Rotations

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.