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A retrodiction paradox in quantum and classical optics

Quantum mechanics represents one of the greatest triumphs of human intellect and, undoubtedly, is the most successful physical theory we have to date. However, since its foundation about a century ago, it has been uninterruptedly the center of harsh debates ignited by the counterintuitive character of some of its predictions. The subject of one of these heated discussions is the so-called "retrodiction paradox", namely a deceptive inconsistency of quantum mechanics which is often associated with the "measurement paradox" and the "collapse of the wave function"; it comes from the apparent time-asymmetry between state preparation and measurement. Actually, in the literature one finds several versions of the retrodiction paradox; however, a particularly insightful one was presented by Sir Roger Penrose in his seminal book \emph{The Road to Reality}. Here, we address the question to what degree Penrose's retrodiction paradox occurs in the classical and quantum domain. We achieve a twofold result. First, we show that Penrose's paradox manifests itself in some form also in classical optics. Second, we demonstrate that when information is correctly extracted from the measurements and the quantum-mechanical formalism is properly applied, Penrose's retrodiction paradox does not manifest itself in quantum optics.