Quantum Phase Distribution and Its Determination

M. Beck, D. T. Smithey, Michael G. Raymer

From the experimental measurement of probability distributions of quadrature-field amplitudes, followed by numerical inversion (optical homodyne tomography), we have determined distributions and/or moments of the optical phase of small-photon-number fields for several definitions of the phase variable, including those based on Hermitian operators and on quasiprobability distributions. These measurements were performed on a vacuum field, and a weakly squeezed field. It is found that each definition of phase yields different distributions and/or moments for the experimental data. In addition, all of the experimentally determined quantities agree with the corresponding theoretical predictions.

Jaewoo Noh

Stephen Mark Barnett, David Thomas Pegg

Experimental determination of the canonical quantum optical phase probability distribution has, until now, required sufficient measurements to determine the complete state of the field. In this Letter we present a more direct means for measuring this distribution which involves synthesizing the projection onto a phase state. Projection synthesis may be applied more generally to measure the probability distribution associated with other observables.

Z. Hradil

Alfredo Luis

We analyze the relation between the classical part of quantum observables and the distributions representing quantum states and observables on the classical phase space. We determine in which conditions such a relation can be established, and the proper phase-space distribution required for this purpose.

Robert Lynch