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Hidden Coherences: Quantum and Classical

Quantum optics and classical optics have coexisted for nearly a century as two descriptions of light, self-consistent in their respective domains.  Recently, detailed examinations have revealed that effects thought to be solely quantum in origin have a place in classical optics. Interference, polarization, coherence, and even entanglement are notions that belong to both quantum and classical optics. A common target in discussions of these matters has often been Niels Bohr's pronouncements and explanations of "complementarity". These have intrigued and challenged philosophers as well as scientists since Bohr's first lecture on the topic in 1927. Complementarity remains the center of the landscape surrounding de Broglie's proposal of particle-wave duality, and interpretive conflicts are still alive. It seems to have escaped notice that a key element in Bohr's own defining summary has never been captured in assessments to date. Here we engage this element and report what we believe to be the first description of complementarity that is unambiguously and quantitatively complete, along with its experimental demonstration.