A new approach to the steering problem for the Schroedinger equation relying on stochastic mechanics and on the theory of Schroedinger bridges is presented. Given the initial and final states psi_0 and psi_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 Schroedinger bridge problem with marginal probability densities | psi_0 |^2 and | psi_1 |^2. This approach is illustrated by working out a simple Gaussian example.
How to steer a quantum system over a Schroedinger bridge
BEGHI, ALESSANDRO;FERRANTE, AUGUSTO;PAVON, MICHELE
2002
Abstract
A new approach to the steering problem for the Schroedinger equation relying on stochastic mechanics and on the theory of Schroedinger bridges is presented. Given the initial and final states psi_0 and psi_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 Schroedinger bridge problem with marginal probability densities | psi_0 |^2 and | psi_1 |^2. This approach is illustrated by working out a simple Gaussian example.File in questo prodotto:
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