Fluctuations of Quantum Entanglement

TL;DR

This paper investigates the stochastic nature of quantum entanglement, quantifying its fluctuations in two-qubit systems, and identifies conditions under which entanglement fluctuations are significant or vanish.

Contribution

It provides the first detailed analysis of entanglement fluctuations in two-qubit systems, including their behavior in pure, mixed, entangled, and separable states.

Findings

Entanglement fluctuations are absent in maximally entangled states.

Regions with fluctuations larger than entanglement are identified.

Fluctuations diverge at entanglement-separability transition points.

Abstract

It is emphasized that quantum entanglement determined in terms of the von Neumann entropy operator is a stochastic quantity and, therefore, can fluctuate. The rms fluctuations of the entanglement entropy of two-qubit systems in both pure and mixed states have been obtained. It has been found that entanglement fluctuations in the maximally entangled states are absent. Regions where the entanglement fluctuations are larger than the entanglement itself (strong fluctuation regions) have been revealed. It has been found that the magnitude of the relative entanglement fluctuations is divergent at the points of the transition of systems from an entangled state to a separable state. It has been shown that entanglement fluctuations vanish in the separable states.