How to Steer a Quantum System over a Schrödinger Bridge

AbstractA 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 ψ0 and ψ1, 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 |ψ0|2 and |ψ1|2. This approach is illustrated by working out a simple Gaussian example. PACS: 03.65.-w

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