Bosonic bunching reveals strong contextual behaviour

Abstract: We show that violation of Klyachko-Can-Binicioglu-Shumovsky [Phys. Rev. Lett. {\bf 101}, 020403 (2008)] pentagram-like inequality can exceed $\sqrt{5}$ provided that exclusive events do not have to be comeasurable and that one uses bosonic systems which exhibit bunching effects. We also show that in this case one can find three pairwise exclusive events whose sum of probabilities is 3/2.