  We report the experimental detection of bulk topological invariants in
nonunitary discrete-time quantum walks with single photons. The nonunitarity of
the quantum dynamics is enforced by periodically performing partial
measurements on the polarization of the walker photon, which effectively
introduces loss to the dynamics. The topological invariant of the nonunitary
quantum walk is manifested in the quantized average displacement of the walker,
which is probed by monitoring the photon loss. We confirm the topological
properties of the system by observing localized edge states at the boundary of
regions with different topological invariants. We further demonstrate the
robustness of both the topological properties and the measurement scheme of the
topological invariants against disorder.
