  One of the common conceptions of nature, typically derived from the
experiences with classical systems, is that attributes of the matter coexist
with the substance. In the quantum regime, however, the quantum particle itself
and its physical property may be in spatial separation, known as the quantum
Cheshire cat effect. While there have been several reports to date on the
observation of the quantum Cheshire cat effect, all such experiments are based
on first-order interferometry and destructive projection measurement, thus
allowing simple interpretation due to measurement-induced disturbance and also
subject to trivial interpretation based on classical waves. In this work, we
report a genuine experimental observation of the quantum Cheshire cat effect
with noninvasive weak quantum measurement as originally proposed. The use of
the weak-measurement probe has allowed us to identify the location of the
single-photon and that of the disembodied polarization state in a quantum
interferometer. We furthermore elucidate the paradox of the quantum Cheshire
cat effect as quantum interference of the transition amplitudes for the photon
and the polarization state which are directly obtained from the measurement
outcomes or the weak values.
