  We address the statistics of a simultaneous CWLM of two non-commuting
variables on a few-state quantum system subject to a conditioned evolution.
Both conditioned quantum measurement and that of two non-commuting variables
differ drastically for either classical or quantum projective measurement, and
we explore the peculiarities brought by the combination of the two.
  We put forward a proper formalism for the evaluation of the distributions of
measurement outcomes. We compute and discuss the statistics in idealized and
experimentally relevant setups. We demonstrate the visibility and
manifestations of the interference between initial and final states in the
statistics of measurement outcomes for both variables in various regimes.
  We analytically predict the peculiarities at the circle ${\cal O}^2_1+{\cal
O}^2_2=1$ in the distribution of measurement outcomes in the limit of short
measurement times and confirm this by numerical calculation at longer
measurement times. We demonstrate analytically anomalously large values of the
time-integrated output cumulants in the limit of short measurement times(sudden
jump) and zero overlap between initial and final states, and give the detailed
distributions. We present the numerical evaluation of the probability
distributions for experimentally relevant parameters in several regimes and
demonstrate that interference effects in the conditioned measurement can be
accurately predicted even if they are small.

Quantum Physics