Quantum correlations and distinguishability of quantum states

TL;DR

This survey reviews key concepts in quantum information, focusing on quantum state distinguishability and correlations, covering mathematical tools and measures used to analyze quantum systems.

Contribution

It provides an up-to-date, comprehensive overview of quantum correlations and state distinguishability, integrating mathematical methods with physical insights.

Findings

Comparison of quantum relative entropies and distances

Analysis of quantum Fisher information and Chernoff bound

Discussion of bipartite entanglement and quantum discord

Abstract

A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination, quantum relative entropies, the Bures distance on the set of quantum states, the quantum Fisher information, the quantum Chernoff bound, bipartite entanglement, the quantum discord, and geometrical measures of quantum correlations. The article is intended both for physicists interested not only by collections of results but also by the mathematical methods justifying them, and for mathematicians looking for an up-to-date introductory course on these subjects, which are mainly developed in the physics literature.