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Published on Sep 2, 2015
This supplemental video for Practical Bayesian Tomography demonstrates using state-space estimation to track a diffusing quantum state. Shown at left is the projection of the true state (star), the sequential Monte Carlo particle cloud (red dots), and covariance approximation to the 99% credible region (red circle) to the x-z plane. Shown at right is a Hinton diagram of the current posterior covariance matrix.
At each time step, each element of the vectorized true state is perturbed by a Gaussian with mean 0 and standard deviation 0.0045, and then is truncated to lie within the space of valid quantum states. The prior over this diffusion rate is taken to be a log-normal distribution with mean 0.006. Each measurement consists of 25 shots along a random Pauli axis.