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A unified approach to entanglement criteria using the Cauchy-Schwarz and Hölder inequalities

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.