Measurement induced chaos with entangled states
  The dynamics of an ensemble of identically prepared two-qubit systems is investigated which is subjected to the iteratively applied measurements and conditional selection of a typical entanglement purification protocol. It is shown that the resulting measurement-induced non-linear dynamics of the two-qubit state exhibits strong sensitivity to initial conditions and also true chaos. For a special class of initially prepared two-qubit states two types of islands characterize the asymptotic limit. They correspond to a separable and a maximally entangled two-qubit state, respectively, and their boundaries form fractal-like structures. In the presence of incoherent noise an additional stable asymptotic cycle appears. 
T. Kiss, S. Vym\v{e}tal, L. D. T\'oth, A. G\'abris, I. Jex, and G.   Alber
quant-ph