  Tunneling of spinless electrons from a single-channel emitter into an empty
collector through an interacting resonant level of the quantum dot (QD) is
studied, when all Coulomb screening of charge variations on the dot is realized
by the emitter channel and the system is mapped onto an exactly solvable model
of a dissipative qubit. In this model we describe the qubit density matrix
evolution with a generalized Lindblad equation, which permit us to count the
tunneling electrons and therefore relate the qubit dynamics to the charge
transfer statistics. In particular, the coefficients of its generating function
equal to the time dependent probabilities to have the fixed number of electrons
tunneled into the collector are expressed through the parameters of a
non-Hermitian Hamiltonian evolution of the qubit pure states in between the
successive electron tunnelings. From the long time asymptotics of the
generating function we calculate Fano factors of the second and third order
(skewness) and establish their relation to the extra average and cumulant,
respectively, of the charge accumulated in the transient process of the empty
QD evolution beyond their linear time dependence. It explains the origin of the
sub and super Poisson shot noise in this system and shows that the super
Poisson signals existence of a non-monotonous oscillating transient current and
the qubit coherent dynamics. The mechanism is illustrated with particular
examples of the generating functions, one of which coincides in the large time
limit with the $1/3$ fractional Poissonian realized without the real fractional
charge tunneling.
