  We investigate the local quantum uncertainty (LQU) between a block of L
qubits and one single qubit in a composite system of n qubits driven through a
quantum phase transition (QPT). A first-order QPT is analytically considered
through a Hamiltonian implementation of the quantum search. In the case of
second-order QPTs, we consider the transverse-field Ising chain via a numerical
analysis through density matrix renormalization group. For both cases, we
compute the LQU for finite-sizes as a function of L and of the coupling
parameter, analyzing its pronounced behavior at the QPT.
