Entanglement witnesses with local partial ordering

TL;DR

This paper introduces a new class of entanglement witnesses based on local partial ordering of observables, providing a framework for their construction and methods for enhancement.

Contribution

It presents a novel framework for entanglement witnesses using local partial ordering and offers techniques to improve their effectiveness.

Findings

Framework for constructing entanglement witnesses

Examples demonstrating the approach

Methods for linear and nonlinear improvements

Abstract

We investigate a class of entanglement witnesses where each witness is formulated as a difference of two product observables. These observables are decomposable into positive semidefinite local operators that obey a partial ordering rule defined over all their possible expectation values. We provide a framework to construct these entanglement witnesses along with some examples. We also discuss methods to improve them both linearly and nonlinearly.