Characterizing (non-)Markovianity through Fisher Information
- URL: http://arxiv.org/abs/2204.04072v5
- Date: Wed, 29 Mar 2023 13:54:59 GMT
- Title: Characterizing (non-)Markovianity through Fisher Information
- Authors: Paolo Abiuso, Matteo Scandi, Dario De Santis, Jacopo Surace
- Abstract summary: Non-Markovian effects are studied by monitoring how information quantifiers evolve in time.
We show that the Fisher information metric emerges as a natural object to study in this context.
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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
Related papers
- Classical Fisher information for differentiable dynamical systems [0.0]
We introduce another classical information, specifically for the deterministic dynamics of isolated, closed, or open classical systems.
This measure of information is defined with Lyapunov vectors in tangent space, making it less akin to the classical Fisher information.
Our analysis of the local state space structure and linear stability lead to upper and lower bounds on this information, giving it an interpretation as the net stretching action of the flow.
arXiv Detail & Related papers (2023-06-28T21:39:09Z) - Nonparametric Identifiability of Causal Representations from Unknown
Interventions [63.1354734978244]
We study causal representation learning, the task of inferring latent causal variables and their causal relations from mixtures of the variables.
Our goal is to identify both the ground truth latents and their causal graph up to a set of ambiguities which we show to be irresolvable from interventional data.
arXiv Detail & Related papers (2023-06-01T10:51:58Z) - Quantum Fisher Information and its dynamical nature [0.0]
This review aims at collecting a number of results scattered in the literature that can be useful to people who begin the study of Fisher information.
We prove that all the physically realisable dynamics can be defined solely in terms of their relation with respect to the Fisher information metric.
arXiv Detail & Related papers (2023-04-28T17:08:44Z) - Interplay between Non-Markovianity of Noise and Dynamics in Quantum
Systems [0.0]
Non-Markovianity of open quantum system dynamics is often associated with the bidirectional interchange of information between the system and its environment.
We have investigated the non-Markovianity of the dynamics of a two-state system driven by continuous time random walk-type noise.
arXiv Detail & Related papers (2023-03-25T19:07:31Z) - Assessing non-Markovian dynamics through moments of the Choi state [0.0]
We provide a criterion for witnessing such non-Markovian dynamics exhibiting information backflow, based on the moments of Choi-matrices.
We present some explicit examples in support of our proposed non-Markovianity detection scheme.
arXiv Detail & Related papers (2023-03-07T03:01:23Z) - Pure non-Markovian evolutions [0.0]
Non-Markovian dynamics are characterized by information backflows.
All non-Markovian evolutions can be divided into two classes: noisy non-Markovian (NNM) and pure non-Markovian (PNM)
arXiv Detail & Related papers (2023-02-09T19:00:02Z) - Preserving quantum correlations and coherence with non-Markovianity [50.591267188664666]
We demonstrate the usefulness of non-Markovianity for preserving correlations and coherence in quantum systems.
For covariant qubit evolutions, we show that non-Markovianity can be used to preserve quantum coherence at all times.
arXiv Detail & Related papers (2021-06-25T11:52:51Z) - OR-Net: Pointwise Relational Inference for Data Completion under Partial
Observation [51.083573770706636]
This work uses relational inference to fill in the incomplete data.
We propose Omni-Relational Network (OR-Net) to model the pointwise relativity in two aspects.
arXiv Detail & Related papers (2021-05-02T06:05:54Z) - Time-Dependent Dephasing and Quantum Transport [68.8204255655161]
We show that non-Markovian dephasing assisted transport manifests only in the non-symmetric configuration.
We find similar results by considering a controllable and experimentally implementable system.
arXiv Detail & Related papers (2021-02-20T22:44:08Z) - Instrumental Variable Value Iteration for Causal Offline Reinforcement Learning [107.70165026669308]
In offline reinforcement learning (RL) an optimal policy is learned solely from a priori collected observational data.
We study a confounded Markov decision process where the transition dynamics admit an additive nonlinear functional form.
We propose a provably efficient IV-aided Value Iteration (IVVI) algorithm based on a primal-dual reformulation of the conditional moment restriction.
arXiv Detail & Related papers (2021-02-19T13:01:40Z) - Movement Tracks for the Automatic Detection of Fish Behavior in Videos [63.85815474157357]
We offer a dataset of sablefish (Anoplopoma fimbria) startle behaviors in underwater videos, and investigate the use of deep learning (DL) methods for behavior detection on it.
Our proposed detection system identifies fish instances using DL-based frameworks, determines trajectory tracks, derives novel behavior-specific features, and employs Long Short-Term Memory (LSTM) networks to identify startle behavior in sablefish.
arXiv Detail & Related papers (2020-11-28T05:51:19Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.