Bell\'s theorem and monogamy

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Quantum entanglement has two remarkable properties. First, according to Bell\'s theorem, the statistical correlations between entangled quantum systems are inconsistent with any theory of local hidden variables. Second, entanglement is monogamous -- that is, to the degree that A and B are entangled with each other, they cannot be entangled with any other systems. It turns out that these properties are intimately related.