NMR investigation of the quantum pigeonhole effect

NMR quantum simulators have been used for studying various quantum phenomena. Here, using a four-qubit NMR quantum simulator, we investigate the recently postulated quantum pigeonhole effect. In this phenomenon, a set of three particles in a two-path interferometer often appears to be in such a superposition that no two particles can be assigned a single path, thus exhibiting the nonclassical behavior. In our experiments, quantum pigeons are emulated by three nuclear qubits whose states are probed jointly and noninvasively by an ancillary spin. The experimental results are in good agreement with quantum theoretical predictions.