In quantum electrodynamics "photons don't have positions". The physical relevance and consequences of this fact has been discussed on this site 1. (Further relevant questions about the concept of photon position: 2, 3, 4, 5). The answer to 1 says that this is a consequence of the Reeh-Schlieder theorem (see e.g. arXiv:1803.04993). It implies the impossibility of having a particle detector that is both reliable and of finite size (and measures for a finite length of time). In the non-relativistic limit, the theorem becomes irrelevant for particles with non-zero rest mass, thus allowing wavefunctions and position operators for things like electrons. The issue with photons is that they have zero rest mass and do not allow such a non-relativistic limit.
The difficulties of localizing particles in relativistic quantum field theory (QFT) have led some to argue against the concept of "particles of light" altogether (see e.g. W. E. Lamb, Jr., “Anti-photon.” Applied Phys B60(1995). Also e.g. arXiv:quant-ph/0103041). On the other hand, in fields such as Quantum Optics and Quantum Information it is common to talk about (distributions of) arrival times and even positions of photons and the concept of a photon wave function has also been proposed (see 2, 3, 4).
My question is: What quantitative limits does QFT imply for a finite size single photon detector measuring for a finite time interval? Such limits might concern things like timing jitter, dark counts and detection efficiency and depend on the spectrum and perhaps other properties of the light being measured, as well as a hypothetical rest mass of the photon, for which we can only achieve an upper bound (see e.g. doi:10.1016/j.physletb.2008.07.018).
I'm assuming these limits are nowhere near the achievable precision of current technology and will perhaps never be achieved for other reasons (practical limitations). Nonetheless, I believe knowing these limits may help understand some fundamental aspects of light and of quantum electrodynamics.
Other relevant questions concerning photon detection: