A textbook interpretation of quantum physics is that quantum objects can be described in a particle or a wave picture, depending on the operations and measurements performed. Beyond this widely held believe, we demonstrate in this contribution that neither the wave nor the particle description is sufficient to predict the outcomes of quantum-optical experiments. To show this, we derive correlation-based criteria that have to be satisfied when either particles or waves are fed into our interferometer. Using squeezed light, it is then confirmed that measured correlations are incompatible with either picture. Thus, within one single experiment, it is proven that neither a wave nor a particle model explains the observed phenomena. Moreover, we formulate a relation of wave and particle representations to two incompatible notions of quantum coherence, a recently discovered resource for quantum information processing.For such an information-theoretic interpretation of our method, we certify the nonclassicality of coherent states - the quantum counterpart to classical waves - in the particle picture, complementing the known fact that photon states are nonclassical in the typically applied wave picture.
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