  The topology of one-dimensional chiral systems is captured by the winding
number of the Hamiltonian eigenstates. Here we show that this invariant can be
read-out by measuring the mean chiral displacement of a single-particle
wavefunction that is connected to a fully localized one via a unitary and
translational-invariant map. Remarkably, this implies that the mean chiral
displacement can detect the winding number even when the underlying Hamiltonian
is quenched between different topological phases. We confirm experimentally
these results in a quantum walk of structured light.
