Perfect single photons cannot be generated on demand due to their infinite tails. To quantify how close realizable states can be to some target single photon, 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. We determine upper and lower bounds for the maximum fidelity in both cases. The bounds are expressed as a function of the size of the target states tails, for negative time or negative frequency respectively.
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