A new approach to the steering problem for the Schrödinger equation relying on stochastic mechanics and on the theory of Schrödinger bridges is presented. Given the initial and final states ψ 0 and ψ 1, respectively, the desired quantum evolution is constructed with the aid of a reference quantum evolution. The Nelson process corresponding to the latter evolution is used as reference process in a Schrödinger bridge problem with marginal probability densities |ψ 0|2 and |ψ 1|2. This approach is illustrated by working out a simple Gaussian example.
Quantum Information Processing – Springer Journals
Published: Oct 13, 2004
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