  Quantum mechanics imposes limits on the statistics of certain observables.
Perhaps the most famous example is the uncertainty principle. Similar
trade-offs also exist for the simultaneous violation of multiple Bell
inequalities. In the simplest case of three observers, it has been shown that
violating one Bell inequality precludes the violation of any other inequality,
a property called monogamy of Bell violations. Forms of Bell monogamy have been
linked to the no-signalling principle and the inability of simultaneous
violations of all inequalities is regarded as their fundamental property. Here
we show that the Bell monogamy does not hold universally and that in fact the
only monogamous situation exists only for three observers. Consequently, the
nature of quantum nonlocality is truly polygamous. We present a systematic
methodology for identifying quantum states and tight Bell inequalities that do
not obey the monogamy principle for any number of more than three observers.
The identified polygamous inequalities are experimentally violated by the
measurement of Bell-type correlations using six-photon Dicke states and may be
exploited for quantum cryptography as well as simultaneous self testing of
multiple nodes in a quantum network.
