From Classical to Quantum Information Geometry: A Guide for Physicists

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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Cited by in corpus (10)

• Witnessing Entanglement and Quantum Correlations in Condensed Matter: A Review
• Noise-Robust Detection of Quantum Phase Transitions
• Extracting Many-Body Quantum Resources within One-Body Reduced Density Matrix Functional Theory
• Quantum geometric protocols for fast high-fidelity adiabatic state transfer
• Quantum geometry in many-body systems with precursors of criticality
• Quantum Fisher information of a cosmic qubit undergoing non-Markovian de Sitter evolution
• Entanglement in the pseudogap regime of cuprate superconductors
• Normal state quantum geometry, non-locality and superconductivity
• Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective
• Information geometry of nonmonotonic quantum natural gradient