Correlations breaking homogenization

The standard collisional model paradigm consists of a system that interacts sequentially with identically prepared ancillas. After infinitely many collisions, and under appropriate conditions, the may converge to same state as This process, known homogenization, is independent ancilla initial state, being property only underlying dynamics. In this paper we extend idea locally identical, but globally correlated, ancillas, show correlations break homogenization. done numerically using minimal qubit model, analytically an exactly soluble Gaussian model. both cases, use Hamiltonian graph states cyclic graphs prototypical method for building scalable many-body entangled ancillary states.