  Weak measurements of photon position can be used to obtain direct
experimental evidence of the wavefunction of a photon between generation and
ultimate detection. Significantly, these measurement results can also be
understood as complex valued conditional probabilities of intermediate photon
positions. It is therefore possible to interpret the quantum state as a complex
valued probability distribution from which measurement probabilities can be
derived according to Bayesian rules. The conventional measurement probabilities
derived from squares of the wavefunction then describes the effects of
measurement back-action, which originate from a non-classical relation between
dynamics and statistics that is characteristic of quantum mechanics. It is
pointed out that this relation can be used to derive the complete Hilbert space
formalism directly from complex probabilities, without the axiomatic
introduction of quantum states or operators.

Quantum Physics