  We show that the bulk winding number characterizing one-dimensional
topological insulators with chiral symmetry can be detected from the
displacement of a single particle, observed via losses. Losses represent the
effect of repeated weak measurements on one sublattice only, which interrupt
the dynamics periodically. When these do not detect the particle, they realize
negative measurements. Our repeated measurement scheme covers both
time-independent and periodically driven (Floquet) topological insulators, with
or without spatial disorder. In the limit of rapidly repeated, vanishingly weak
measurements, our scheme describes non-Hermitian Hamiltonians, as the lossy
Su-Schrieffer-Heeger model of Phys. Rev. Lett. 102, 065703 (2009). We find,
contrary to intuition, that the time needed to detect the winding number can be
made shorter by decreasing the efficiency of the measurement. We illustrate our
results on a discrete-time quantum walk, and propose ways of testing them
experimentally.
