How to Steer a Quantum System over a Schrödinger Bridge

  • Authors:

  • Alessandro Beghi;Augusto Ferrante;Michele Pavon

  • Affiliations:

  • Dipartimento di Elettronica e Informatica, Università di Padova, via Gradenigo 6/A, 35131 Padova, Italy. E-mail: beghi@dei.unipd.it;Dipartimento di Elettronica e Informatica, Università di Padova, via Gradenigo 6/A, 35131 Padova, Italy. E-mail: augusto@dei.unipd.it;Dipartimento di Matematica Pura e Applicata, Università di Padova and LADSEB-CNR, via Belzoni 7, 35131 Padova, Italy. E-mail: michele.pavon@unipd.it

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2002

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Abstract

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 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