Exact solution for the evolution of a qubit under continuous measurement
Résumé
We analyze an experiment with continuous heterodyne measurement of an energy loss operator on a superconducting qubit. We have observed that in the associated mathematical model, due to the degeneracy of the diffusion operator, the resulting quantum trajectories are supported not in the entire Bloch sphere, but instead they belong to the surface of a deterministically evolving ellipsoid. This allows to analytically solve for the probability distribution of the prior-to-measurement quantum state, governed by the stochastic differential master equation.
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