Entanglement-fluctuation relation for bipartite pure states

TL;DR

This paper establishes a relation between subsystem fluctuations and entanglement in bipartite pure states, offering a way to measure entanglement experimentally through polarization fluctuations.

Contribution

It introduces a generalized polarization fluctuation measure that quantifies entanglement and relates it to subsystem purity, applicable to various quantum systems.

Findings

Fluctuations correlate with entanglement measures in bipartite states.

Derived relations are tested on fermion gas and spin chain models.

Framework enables experimental entanglement measurement using polarization fluctuations.

Abstract

We identify subsystem fluctuations (variances) that measure entanglement in an arbitrary bipartite pure state. These fluctuations are of observables that generalize the notion of polarization to an arbitrary N-level subsystem. We express this polarization fluctuation in terms of subsystem purity and other entanglement measures. The derived fluctuation-entanglement relation is evaluated for the ground states of a one-dimensional free fermion gas and the Affleck-Kennedy-Lieb-Tasaki spin chain. Our results provide a framework for experimentally measuring entanglement using Stern-Gerlach-type state selectors.