So far, most of the attention of studies on quantum chaos has focused on the maximal Lyapunov exponent. Classically, however, that are several quantifiers to study chaotic dynamics. For instance, the generalised Lyapunov exponent (GLE) accounts for chaotic fluctuations of the dynamical system. Its non-trivial behaviour is associated with multifractality. This research objective is to derive bounds for the quantum GLE and to use them to study quantum multifractality.