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Schrödinger bridges: classical and quantum evolution

Presented by: 
T Georgiou University of Minnesota
Monday 11th August 2014 - 10:00 to 11:00
INI Seminar Room 2

The classical Schrödinger bridge seeks the most likely probability law for a diffusion process, in path space, that matches marginals at two end points in time' a problem with deep connection to stochastic optimal control. In the talk, we begin with a historic account of Schrödinger's initial motivation and theory, we discuss in detail the special case of Schrödinger bridges for Markov chains where we explain a constructive approach for the existence and uniqueness based on the Hilbert metric, we present a generalization of Schrödinger bridges for quantum channels, and finally, we return to a classical context and discuss an extension to degenerate linear diffusions and the problem to steer the distribution of the state of a linear stochastically driven dynamical system.

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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons