Entanglement versus mutual information in quantum spin chains

TL;DR

This paper compares quantum entanglement and classical mutual information in a quantum Ising chain, revealing similar scaling behaviors and establishing an inequality that mutual information does not exceed entanglement.

Contribution

It demonstrates that mutual information of classical spin configurations shares the same scaling form as quantum entanglement in a conformally invariant system and proves the inequality I ≤ E.

Findings

Mutual information obeys the same scaling form as entanglement at criticality.

The inequality I ≤ E holds in both ground state and dynamic evolution.

Mutual information is generally bounded above by entanglement in bipartite pure states.

Abstract

The quantum entanglement $E$ of a bipartite quantum Ising chain is compared with the mutual information $I$ between the two parts after a local measurement of the classical spin configuration. As the model is conformally invariant, the entanglement measured in its ground state at the critical point is known to obey a certain scaling form. Surprisingly, the mutual information of classical spin configurations is found to obey the same scaling form, although with a different prefactor. Moreover, we find that mutual information and the entanglement obey the inequality $I\leq E$ in the ground state as well as in a dynamically evolving situation. This inequality holds for general bipartite systems in a pure state and can be proven using similar techniques as for Holevo's bound.