  Exact single photons cannot be generated on demand due to their infinite
tails. To quantify how close realizable optical states can be to some target
single photon in one dimension, we argue that there are two natural but
incompatible ways to specify the target state. Either it can be expressed as a
photon with a chosen positive-frequency spectrum, or it can be described as an
(unphysical) photon in a chosen positive-time pulse. The results show that for
sufficiently short target pulses, the closest realizable states contain
substantial multiphoton components. Upper and lower bounds for the maximum
fidelity are derived and are expressed as functions of the size of the target
state's tail, for negative time or negative frequency, respectively. We also
generalize the bounds to arbitrary photon-number states.
