  A number of physically intuitive results for the calculation of multi-time
correlations in phase-space representations of quantum mechanics are obtained.
They relate time-dependent stochastic samples to multi-time observables, and
rely on the presence of derivative-free operator identities. In particular,
expressions for time-ordered normal-ordered observables in the positive-P
distribution are derived which replace Heisenberg operators with the bare
time-dependent stochastic variables, confirming extension of earlier such
results for the Glauber-Sudarshan P. Analogous expressions are found for the
anti-normal-ordered case of the doubled phase-space Q representation, along
with conversion rules among doubled phase-space s-ordered representations. The
latter are then shown to be readily exploited to further calculate anti-normal
and mixed-ordered multi-time observables in the positive-P, Wigner, and
doubled-Wigner representations. Which mixed-order observables are amenable and
which are not is indicated, and explicit tallies are given up to 4th order.
Overall, the theory of quantum multi-time observables in phase-space
representations is extended, allowing non-perturbative treatment of many cases.
The accuracy, usability, and scalability of the results to large systems is
demonstrated using stochastic simulations of the unconventional photon blockade
system and a related Bose-Hubbard chain. In addition, a robust but simple
algorithm for integration of stochastic equations for phase-space samples is
provided.
