  We present a theoretical framework based on second quantization in Liouville
space to treat open quantum systems. We consider an ensemble of identical
quantum emitters characterized by a discrete set of quantum states. The second
quantization is performed directly at the level of density matrices, thereby
significantly reducing the size of the Liouville space. In contrast to
conventional Hilbert space techniques, statistically mixed states and
dissipation are naturally incorporated. As a particular example of application,
we study the effect of incoherent processes and statistical mixing of emitters'
initial states in the interaction with quantum light. Moreover, we link our
framework to a phase-space description of the dynamics, which can overcome the
computational limitations of our method with the increasing number of
particles.
