Quantitative entanglement witnesses of Isotropic- and Werner-class via local measurements

TL;DR

This paper introduces a method to quantify entanglement in Werner- and Isotropic-class states using local measurements, leveraging twirling transformations for optimal bounds and classical post-processing to improve accuracy, with applications in quantum optics.

Contribution

It presents a new approach to derive tight entanglement bounds for specific states using local measurements and classical data processing, simplifying experimental procedures.

Findings

Optimal bounding functions derived from twirling transformations.

Local decompositions enable efficient classical post-processing.

Application to quantum optics with hyper-entanglement schemes.

Abstract

Quantitative entanglement witnesses allow one to bound the entanglement present in a system by acquiring a single expectation value. In this paper we analyze a special class of such observables which are associated with (generalized) Werner and Isotropic states. For them the optimal bounding functions can be easily derived by exploiting known results on twirling transformations. By focusing on an explicit local decomposition for these observables we then show how simple classical post-processing of the measured data can tighten the entanglement bounds. Quantum optics implementations based on hyper-entanglement generation schemes are analyzed.