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Quantum Fisher information and its dynamical nature.

Matteo Scandi1,2, Paolo Abiuso2,3, Jacopo Surace2,4

  • 1Instituto de Física Teórica UAM/CSIC, C/ Nicolás Cabrera 13-15, 28049 Cantoblanco, Madrid, Spain.

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Summary

This review consolidates research on Fisher information metrics and their quantum generalizations. It reveals the inherent dynamical nature of Fisher information, linking it to physical evolution properties.

Keywords:
information geometrymathematical physicsquantum information

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Area of Science:

  • Quantum Information Theory
  • Statistical Mechanics
  • Metrology

Background:

  • Fisher information metrics and their quantum generalizations are crucial in diverse fields like hypothesis testing, metrology, and thermodynamics.
  • Despite broad applications, only a limited set of quantum Fisher informations are extensively studied.
  • Existing literature presents scattered results, hindering a cohesive understanding of the topic.

Purpose of the Study:

  • To compile scattered results on Fisher information and its quantum generalizations.
  • To provide a unified treatment for both beginners and experts in the field.
  • To explore novel connections between Fisher information and physical evolutions.

Main Methods:

  • Literature review and synthesis of existing research on Fisher information.
  • Introduction of new results connecting Fisher information to dynamical properties.
  • Analysis of the relationship between Fisher information metrics and physical evolution maps.

Main Results:

  • The review offers a cohesive overview of Fisher information and its quantum variants.
  • New findings demonstrate that dynamical properties (positivity, Markovianity, detailed balance, retrodictive power) can be characterized by their relation to Fisher information metrics.
  • Fisher information possesses an inherent dynamical nature, a fact previously underestimated in the literature.

Conclusions:

  • Fisher information metrics are fundamental tools with wide-ranging applications.
  • Understanding the dynamical nature of Fisher information is key to characterizing physical evolutions.
  • This work provides a comprehensive resource and novel insights into Fisher information and its connection to quantum dynamics.