Highly-efficient estimation of entanglement measures for large experimentally created graph states via simple measurements

TL;DR

This paper introduces a method to efficiently estimate entanglement measures in large two-colorable graph states using only stabilizer measurements, significantly reducing measurement complexity.

Contribution

The authors develop analytical techniques to quantify entanglement in large graph states from simple stabilizer measurements, bypassing full density matrix reconstruction.

Findings

Analytical results for robustness of entanglement.

Analytical results for relative entropy of entanglement.

Exponential reduction in measurement requirements.

Abstract

Quantifying experimentally created entanglement could in principle be accomplished by measuring the entire density matrix and calculating an entanglement measure of choice thereafter. Due to the tensor-structure of the Hilbert space, this approach becomes infeasible even for medium-size systems. In this letter we present methods to quantify the entanglement of arbitrarily large two-colorable graph states from simple measurements. The measurement data considered here is merely given by stabilizer measurements, thus leading to an exponential reduction in the number of measurements required. We provide analytical results for the robustness of entanglement and the relative entropy of entanglement.