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Standard quantum physics prevents the existence of a joint statistics forcomplementary observables. Nevertheless, a joint distribution for complementaryobservables can be derived from their imperfect simultaneous measurementfollowed by a suitable data inversion. Quantumness is reflected then in thepathologies of the inferred distribution. We apply this program to theparadigmatic example of complementarity: the wave-particle duality in a Younginterferometer.

Complementarity and the pathological statistics of the quantum impossible