  We introduce quantum versions of the Kac Master Equation and the Kac
Boltzmann Equation. We study the steady states of each of these equations, and
prove a propagation of chaos theorem that relates them. The Quantum Kac Master
Equation (QKME) describes a quantum Markov semigroup, while the Kac Boltzmann
Equation describes a non-linear evolution of density matrices on the single
particle state space. All of the steady states of the $N$ particle quantum
system described by the QKME are separable, and thus the evolution described by
the QKME is entanglement breaking. The results set the stage for a quantitative
study of approach to equilibrium in quantum kinetic theory, and a quantitative
study the rate of destruction of entanglement in a class of quantum Markov
semigroups describing binary interactions.
