In this introductory talk the role of information theory in the description of physical evolutions will be discussed. After defining information quantifiers, their contractivity with respect to stochastic dynamics will be explained, a requirement which simply encodes the intuition that noisy transformations should lose information. The interplay between the two concepts will be exemplified for Markovian evolutions, showing how Markovianity can be defined in purely information theoretic terms. Extending on this result, we prove our main theorem: that all physical maps can be defined solely in terms of a particular metric on the space of probability distributions, the Fisher information. This result proves once again the foundational role of information theory in physics.
Presential in the seminar room. Zoom stream:
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