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Characterizing (non-)Markovianity through Fisher Information

by Paolo Abiuso, Matteo Scandi, Dario De Santis, Jacopo Surace

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Submission summary

Authors (as registered SciPost users): Paolo Abiuso
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-05-22
Date submitted: 2023-03-30 14:09
Submitted by: Abiuso, Paolo
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Quantum Physics
Approach: Theoretical


A non-isolated physical system typically loses information to its environment, and when such loss is irreversible the evolution is said to be Markovian. Non-Markovian effects are studied by monitoring how information quantifiers, such as the distance between physical states, evolve in time. Here we show that the Fisher information metric emerges as a natural object to study in this context; we fully characterize the relation between its contractivity properties and Markovianity, both from the mathematical and operational point of view. We prove, both for classical and quantum dynamics, that Markovianity is equivalent to the monotonous contraction of the Fisher metric at all points of the set of states. At the same time, operational witnesses of non-Markovianity based on the dilation of the Fisher distance cannot, in general, detect all non-Markovian evolutions, unless specific physical postprocessing is applied to the dynamics. Finally, we show for the first time that non-Markovian dilations of Fisher distance between states at any time correspond to backflow of information about the initial state of the dynamics at time 0, via Bayesian retrodiction.

Author comments upon resubmission

Dear Editor and Referees,
Thank you for assessing our work.
After the latest round of reports, we hereby resubmit the final version of the paper with minor revision.
As suggested by Referee 1, we included a comment - footnote 5, below Eq.(27) - to connect the specific example we use in the main text (to showcase some of our results) to known amplitude damping channels with thermal asymptotic states.

Best regards,
The Authors.

Published as SciPost Phys. 15, 014 (2023)

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