Quantifying entanglement of maximal dimension in bipartite mixed states

TL;DR

This paper develops a framework to quantify the maximum Schmidt number in bipartite mixed states using minimal local measurements, with implications for multipartite entanglement assessment.

Contribution

It introduces a novel method to lower bound G-concurrence in mixed states with few measurements, advancing entanglement quantification techniques.

Findings

Framework for lower bounding G-concurrence

Applicable to multipartite states

Requires only few local measurements

Abstract

The Schmidt coefficients capture all entanglement properties of a pure bipartite state and therefore determine its usefulness for quantum information processing. While the quantification of the corresponding properties in mixed states is important both from a theoretical and a practical point of view, it is considerably more difficult, and methods beyond estimates for the concurrence are elusive. In particular this holds for a quantitative assessment of the most valuable resource, the maximum possible Schmidt number of an arbitrary mixed state. We derive a framework for lower bounding the appropriate measure of entanglement, the so-called G-concurrence, through few local measurements. Moreover, we show that these bounds have relevant applications also for multipartite states.