In my previous post on linear optics quantum computing (LOQC) I discussed the notion of interfering photons, which is a fundamental requirement for LOQC. It turns out that for photons to interfere they must be indistinguishable. In quantum mechanics the term indistinguishable has a very strict interpretation: if we have two photons, there must be no way, in principle, for us to tell them apart. For example, suppose we had two identical photons arriving one after another. In this case, the different timing of the two photons allows us to know which is which. Thus, the photons are temporally distinguishable. Simlilarly, two photons might arrive simultaneously, but be spatially separated, in which case the photons are also distinguishable. Experimentally, making photons which are completely indistinguishable is extremely challenging and requires an enormous amount of precision, which is limited by technology. This problem of making indistinguishable photons is one of the most significant complications facing experimentalists.
In this paper we analysed the effect of photon distinguishability on the operation of LOQC circuits, in particular the controlled-NOT (CNOT) gate, which I described in an earlier post. From this analysis we were able to specify how distinguishable photons need to be for an experimental CNOT gate to work effectively. Understanding this is clearly very important from an experimental point of view, since it gives us an idea of how well we can reasonably expect our experimental gates to work.