  The geometric (Berry-Pancharatnam) phase originates from the intrinsic
geometry of the space of quantum states and can be observed in different
situations, such as a cyclic evolution of a quantum system. Here, we utilize
the geometric phase to obtain a surprising insight: It is possible to create
nonlocal correlations in a fixed interferometer with independent photon inputs
by varying the photons' internal states.In particular, we consider a cyclic
interferometer that is fixed, i.e., that has no variable internal phase shifts
or subsequent measurement settings. Instead, the measurement choices of the
different parties correspond to the internal states of the input photons which
influence the observed correlations via a collective $N$-photon geometric
phase, constituting a different approach for the generation of nonlocality with
respect to the usual paradigm. We observe a trade-off between the geometric
phases and the visibility of the many-photon interference, impeding the
generation of nonlocality. However, by making use of the dynamical quantum Zeno
effect, we show that nonlocality can be created in the fixed cyclic
interferometer using 12 (or more) independent photons.
