Monogamy of quantum entanglement and other correlations

It has been observed by numerous authors that a quantum system being entangled with another one limits its possible entanglement with a third system: this has been dubbed the ``monogamous nature of entanglement.'' In this paper we present a simple identity which captures the trade off between entanglement and classical correlation, which can be used to derive rigorous monogamy relations. We also prove various other trade offs of a monogamy nature for other entanglement measures and secret and total correlation measures.