  We analyze the consequences of iterative measurement-induced nonlinearity on
the dynamical behavior of qubits. We present a one-qubit scheme where the
equation governing the time evolution is a complex-valued nonlinear map with
one complex parameter. In contrast to the usual notion of quantum chaos,
exponential sensitivity to the initial state occurs here. We calculate
analytically the Lyapunov exponent based on the overlap of quantum states, and
find that it is positive. We present a few illustrative examples of the
emerging dynamics.
