A unified approach to entanglement criteria using the Cauchy-Schwarz and H\"older inequalities

TL;DR

This paper introduces a unified framework for entanglement criteria based on the Cauchy-Schwarz and H"older inequalities, revealing connections among existing criteria and enabling the derivation of new ones for bipartite and multipartite entanglement detection.

Contribution

It provides a general principle unifying various entanglement criteria and systematically explores its effectiveness and limitations.

Findings

Unified entanglement criteria derived from Cauchy-Schwarz and H"older inequalities.

New entanglement detection criteria proposed.

Analysis of the potential and limits of the unified approach.

Abstract

We present unified approach to different recent entanglement criteria. Although they were developed in different ways, we show that they are all applications of a more general principle given by the Cauchy-Schwarz inequality. We explain this general principle and show how to derive with it not only already known but also new entanglement criteria. We systematically investigate its potential and limits to detect bipartite and multipartite entanglement.