Lower bounds on entanglement measures from incomplete information

TL;DR

This paper develops methods to estimate quantum entanglement measures from limited experimental data, such as a single observable expectation value, using Legendre transforms and analytical techniques.

Contribution

It introduces new algorithms and analytical approaches for estimating entanglement measures from incomplete information, including concurrence and geometric measure.

Findings

Algorithm for concurrence estimation

Analytical bounds for geometric entanglement

Comparison with existing methods shows improved estimates

Abstract

How can we quantify the entanglement in a quantum state, if only the expectation value of a single observable is given? This question is of great interest for the analysis of entanglement in experiments, since in many multiparticle experiments the state is not completely known. We present several results concerning this problem by considering the estimation of entanglement measures via Legendre transforms. First, we present a simple algorithm for the estimation of the concurrence and extensions thereof. Second, we derive an analytical approach to estimate the geometric measure of entanglement, if the diagonal elements of the quantum state in a certain basis are known. Finally, we compare our bounds with exact values and other estimation methods for entanglement measures.