Quantum violation of the pigeonhole principle and the nature of quantum correlations

The pigeonhole principle: “If you put three pigeons in two pigeon-holes, at least two of the pigeons end up in the same hole,” is an obvious yet fundamental principle of nature as it captures the very essence of counting. Here however we show that in quantum mechanics this is not true! We find instances when three quantum particles are put in two boxes, yet no two particles are in the same box.