Unified approach to geometric and positive-map-based non-linear entanglement identifiers

TL;DR

This paper explores the relationship between positive map-based and geometric entanglement identifiers, proposing a unified framework for nonlinear criteria that are more experimentally accessible.

Contribution

It establishes a fundamental link between two major entanglement detection methods and introduces a new framework for nonlinear, experimentally friendly entanglement criteria.

Findings

Found a profound relation between positive map and geometric entanglement identifiers.

Proposed a general framework for nonlinear entanglement criteria.

Enabled construction of new experimentally friendly entanglement detection methods.

Abstract

Detecting quantumness of correlations (especially entanglement) is a very hard task even in the simplest case i.e. two-partite quantum systems. Here we provide an analysis whether there exists a relation between two most popular types of entanglement identifiers: the first one based on positive maps and not directly applicable in laboratory and the second one --- geometric entanglement identifier which is based on specific Hermiticity-preserving maps. We show a profound relation between those two types of entanglement criteria. Hereunder we have proposed a general framework of nonlinear functional entanglement identifiers which allows us to construct new experimentally friendly entanglement criteria.