  We propose a quantum version of a gedanken experiment which supports the
generalized second law of black hole thermodynamics. A quantum measurement of
particles in the region outside of the event horizon decreases the entropy of
the outside matter due to the entanglement of the inside and outside particle
states. This decrease is compensated, however, by the increase in the detector
entropy. If the detector is conditionally dropped into the black hole depending
on the experimental outcome, the decrease of the matter entropy is more than
compensated by the increase of the black hole entropy via the increase of the
black hole mass which is ultimately attributed to the work done by the
measurement.
