  General quasi-probabilities are introduced to visualize time-dependent
quantum correlations of light in phase space. They are based on the
generalization of the Glauber-Sudarshan P function to a time-dependent P
functional [W. Vogel, Phys. Rev. Lett. 100, 013605 (2008)], which fully
describes temporal correlations of radiation fields on the basis of continuous
phase-space distributions. This approach is nontrivial as the P functional
itself is highly singular for many quantum states and nonlinear processes. In
general, it neither yields a well-behaved nor an experimentally accessible
description of quantum stochastic processes. Our regularized version of this
multi-time-dependent quasi-probability is a smooth function and applies to
stronger divergences compared to the single-time and multi-mode scenario. The
technique is used to characterize an optical parametric process with frequency
mismatch. A measurement scheme, together with a sampling approach, is provided
which yields direct experimental access to the regularized P functional from
measured data.
