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We present unified approach to different recent entanglement criteria.Although they were developed in different ways, we show that they are allapplications of a more general principle given by the Cauchy-Schwarzinequality. We explain this general principle and show how to derive with itnot only already known but also new entanglement criteria. We systematicallyinvestigate its potential and limits to detect bipartite and multipartiteentanglement.

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