Relationship between semiclassical and quantum-mechanical input-output theories of optical response

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Abstract
We discuss the relationship between fully quantized and semiclassical approaches to input-output theory that connect asymptotically free fields prior to and following interactions that we describe in terms of canonical transformations. We demonstrate the utility of the Wigner function in describing the connection between input and output fields, and show how it is particularly well suited to describe many quantum-optical systems in terms of positive quasiprobability permitting classical stochastic simulation.