  We introduce a quantum version for the statistical complexity measure, in the
context of quantum information theory, and use it as a signalling function of
quantum order-disorder transitions. We discuss the possibility for such
transitions to characterize interesting physical phenomena, as quantum phase
transitions, or abrupt variations in the correlation distributions. We apply
our measure to two exactly solvable Hamiltonian models, namely: the
$1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also
compute this measure for one-qubit and two-qubit reduced states for the
considered models, and analyse its behaviour across its quantum phase
transitions for finite system sizes as well as in the thermodynamic limit by
using Bethe ansatz.
