  We deal with a system comprising a nonlinear (Kerr-like) oscillator excited
by a series of ultra-short external pulses. We introduce the fidelity-based
entropic parameter that can be used as an indicator of quantum chaos. Moreover,
we propose to use the fidelity-like parameter comprising the information about
the mean number of photons in the system. We shall concentrate on the long-time
behaviour of the parameters discussed, showing that for deep chaos cases the
quantum fidelities behave chaotically in the classical sense despite their
strictly quantum character.
