title: Observing Dirac's classical phase space analog to the quantum state.
abstract: In 1945, Dirac attempted to develop a “formal probability” distribution to describe quantum operators in terms of two noncommuting variables, such as position x and momentum p [Rev. Mod. Phys. 17, 195 (1945)]. The resulting quasiprobability distribution is a complete representation of the quantum state and can be observed directly in experiments. We measure Dirac’s distribution for the quantum state of the transverse degree of freedom of a photon by weakly measuring transverse x so as to not randomize the subsequent p measurement. Furthermore, we show that the distribution has the classical-like feature that it transforms (e.g., propagates) according to Bayes’ law.
authors.affiliation: Measurement Science and Standards, National Research Council, Ottawa, Canada K1A 0R6.
authors.forename: Charles
authors.initials: C
authors.lastname: Bamber
authors.affiliation: Physics Department, University of Ottawa, 150 Louis Pasteur, Ottawa, Canada K1N 6N5.
authors.forename: Jeff S
authors.initials: JS
authors.lastname: Lundeen