From Classical to Quantum Information Geometry: A Guide for Physicists
- URL: http://arxiv.org/abs/2302.13515v3
- Date: Fri, 30 Jun 2023 23:13:34 GMT
- Title: From Classical to Quantum Information Geometry: A Guide for Physicists
- Authors: J. Lambert, E. S. S{\o}rensen
- Abstract summary: The study of topological phases of matter characterized by Chern number is rooted in the symplectic structure of the quantum state space.
The fidelity susceptibility has gained prominence as a universal probe of quantum criticality.
The study of quantum Fisher information in many body systems has seen a surge of interest due to its role as a witness of genuine multipartite entanglement.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Recently, there has been considerable interest in the application of
information geometry to quantum many body physics. This interest has been
driven by three separate lines of research, which can all be understood as
different facets of quantum information geometry. First, the study of
topological phases of matter characterized by Chern number is rooted in the
symplectic structure of the quantum state space, known in the physics
literature as Berry curvature. Second, in the study of quantum phase
transitions, the fidelity susceptibility has gained prominence as a universal
probe of quantum criticality, even for systems that lack an obviously
discernible order parameter. Finally, the study of quantum Fisher information
(QFI) in many body systems has seen a surge of interest due to its role as a
witness of genuine multipartite entanglement and owing to its utility as a
quantifier of quantum resources, in particular those useful in quantum sensing.
Rather than a thorough review, our aim is to connect key results within a
common conceptual framework that may serve as an introductory guide to the
extensive breadth of applications, and deep mathematical roots, of quantum
information geometry, with an intended audience of researchers in quantum many
body and condensed matter physics.
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