Hyperfine Structure of Quantum Entanglement

TL;DR

This paper introduces the hyperfine structure of entanglement, a new measure decomposing entanglement contours into particle-number cumulants, revealing universal properties and applications across various quantum systems.

Contribution

It presents the hyperfine structure of entanglement as a novel measure with universal properties, applicable to diverse quantum systems and providing deeper insights into quantum entanglement.

Findings

Establishes connections between hyperfine structure and mutual information in Fermi gases.

Unveils finer subregion-subregion duality in AdS$_3$/CFT$_2$ correspondence.

Distinguishes topological from trivial gapped states in Chern insulators.

Abstract

Quantum entanglement, crucial for understanding quantum many-body systems and quantum gravity, is commonly assessed through various measures such as von Neumann entropy, mutual information, and entanglement contour, each with its inherent advantages and limitations. In this work, we introduce the hyperfine structure of entanglement, which decomposes entanglement contours known as the fine structure into particle-number cumulants. This measure exhibits a set of universal properties with its significance in quantum information science. We apply it across diverse contexts: in Fermi gases, establishing connections to mutual information and interacting conformal field theory; in AdS$_3$/CFT$_2$ correspondence, unveiling finer subregion-subregion duality; and in Chern insulators, distinguishing between different quantum phases, especially topological gapped state and trivial gapped state. Our findings suggest experimental accessibility, offering fresh insights into quantum entanglement across physical systems.