Quantum retrodiction.

Quantum retrodiction, in which the state of a quantum system prior to a measurement is assigned based on the results of that measurement, has had a long history and has been used in quantum optics research for decades. Here we summarize the theory and point out some of the more interesting results, before applying the theory to state identification from multiple shots of an experiment. One surprising result is that we show that a photodetector with low quantum efficiency can discriminate between photonic states better than a detector with a higher efficiency.This article is part of the theme issue 'The quantum theory of light'.