  A single photon incident on a beam splitter produces an entangled field
state, and in principle could be used to violate a Bell-inequality, but such an
experiment (without post-selection) is beyond the reach of current experiments.
Here we consider the somewhat simpler task of demonstrating EPR-steering with a
single photon (also without post-selection). That is, of demonstrating that
Alice's choice of measurement on her "half" of a single photon can affect the
other "half" of the photon in Bob's lab, in a sense rigorously defined by us
and Doherty [Phys. Rev. Lett. 98, 140402 (2007)]. Previous work by Lvovsky and
co-workers [Phys. Rev. Lett. 92, 047903 (2004)] has addressed this phenomenon
(which they called "remote preparation") experimentally using homodyne
measurements on a single photon. Here we show that, unfortunately, their
experimental parameters do not meet the bounds necessary for a rigorous
demonstration of EPR-steering with a single photon. However, we also show that
modest improvements in the experimental parameters, and the addition of photon
counting to the arsenal of Alice's measurements, would be sufficient to allow
such a demonstration.
