Witnessing Entanglement and Quantum Correlations in Condensed Matter: A Review

TL;DR

This review discusses recent advances in detecting and certifying entanglement and quantum correlations in condensed matter systems, emphasizing measurement techniques, theoretical frameworks, and future research directions.

Contribution

It provides a comprehensive overview of entanglement witnesses and quantum correlation measures applied to condensed matter, connecting theory with experimental techniques and exploring future prospects.

Findings

Development of frameworks linking measurements to entanglement in materials

Analysis of quantum correlation measures like quantum Fisher information and discord

Discussion of experimental techniques such as susceptibility and spectroscopic methods

Abstract

The detection and certification of entanglement and quantum correlations in materials is of fundamental and far-reaching importance, and has seen significant recent progress. It impacts both our understanding of the basic science of quantum many-body phenomena as well as the identification of systems suitable for novel technologies. Frameworks suitable to condensed matter that connect measurements to entanglement and coherence have been developed in the context of quantum information theory. These take the form of entanglement witnesses and quantum correlation measures. The underlying theory of these quantities, their relation to condensed matter experimental techniques, and their application to real materials are comprehensively reviewed. In addition, their usage in e.g. protocols, the relative advantages and disadvantages of witnesses and measures, and future prospects in, e.g., correlated electrons, entanglement dynamics, and entangled spectroscopic probes, are presented. Consideration is given to the interdisciplinary nature of this emerging research and substantial ongoing progress by providing an accessible and practical treatment from fundamentals to application. Particular emphasis is placed on quantities accessible to collective measurements, including by susceptibility and spectroscopic techniques. This includes the magnetic susceptibility witness, one-tangle, concurrence and two-tangle, two-site quantum discord, and quantum coherence measures such as the quantum Fisher information.