Fractals in Quantum Information Process

In the recent work of Kiss et al.[Phys.Rev.Lett.107(2011)100501],the evolvement of two-qubit quantum states in a measurement-based purification process is studied.As they pointed out,the purification results manifest sensitivity to the applied initial states.The convergence regions to different stable circles are depicted on a complex plane.Because of the result patterns'likeness to typical fractals,we make further study on the interesting patterns'connection to fractals.Finally,through a numerical method we conclude that the boundaries of different islands of the patterns are fractals,which possess a non-integral fractal dimension.Also,we show that the fractal dimension would vary with the change of the portion of the noise added to the initial states.