  A nonclassical state of light is distributed, via a beam splitter, between
two remote parties. One of the parties applies the photon annihilation operator
to its portion of the state. Surprisingly, this local intervention removes a
photon from the entire initial state, leaving its mode as well as the spatial
and temporal structure undisturbed. In this way, nonlocal quantum
action-at-a-distance occurs without local state collapse by either party. This
leads to curious consequences, such as the absence of a shadow when the
annihilation operator is applied to a part of the spatial cross-section of the
initial optical mode. In the experiment, we subtract a single photon from a
part of an optical mode initially prepared in the one- or two-photon Fock
state. Subsequent homodyne tomography reveals that the whole mode has jumped to
the next lower Fock state, with no change in the mode shape.
