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How to Steer a Quantum System over a Schrödinger Bridge

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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 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.

PACS: 03.65.-w

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Authors and Affiliations

  1. Dipartimento di Elettronica e Informatica, Università di Padova, via Gradenigo 6/A, 35131, Padova, Italy

    Alessandro Beghi & Augusto Ferrante

  2. Dipartimento di Matematica Pura e Applicata, Università di Padova and LADSEB-CNR, via Belzoni 7, 35131, Padova, Italy

    Michele Pavon

Authors
  1. Alessandro Beghi
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  2. Augusto Ferrante
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  3. Michele Pavon
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Beghi, A., Ferrante, A. & Pavon, M. How to Steer a Quantum System over a Schrödinger Bridge. Quantum Information Processing 1, 183–206 (2002). https://doi.org/10.1023/A:1019873024970

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