  We investigate the violation of local realism in Bell tests involving
homodyne measurements performed on multimode continuous-variable states. By
binning the measurement outcomes in an appropriate way, we prove that the
Mermin-Klyshko inequality can be violated by an amount that grows exponentially
with the number of modes. Furthermore, the maximum violation allowed by quantum
mechanics can be attained for any number of modes, albeit requiring a quantum
state that is rather unrealistic. Interestingly, this exponential increase of
the violation holds true even for simpler states, such as multipartite GHZ
states. The resulting benefit of using more modes is shown to be significant in
practical multipartite Bell tests by analyzing the increase of the robustness
to noise with the number of modes. In view of the high efficiency achievable
with homodyne detection, our results thus open a possible way to feasible
loophole-free Bell tests that are robust to experimental imperfections. We
provide an explicit example of a three-mode state (a superposition of coherent
states) which results in a significantly high violation of the Mermin-Klyshko
inequality (around 10%) with homodyne measurements.
