Quantum vampire: collapse-free action at a distance by the photon annihilation operator

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.