Decoherence of a 2-Path System by Infrared Photons

We calculate the decoherence caused by photon emission for a charged particle travelling through an interferometer; the decoherence rate gives a quantitative measure of how much "which-path" quantum information is gained by the electromagnetic field. We isolate the quantum information content of both leading and sub-leading soft photons, and show that it can be extracted entirely from information about the endpoints of the particle's paths. When infrared dressing is used to cure the infrared divergences in the theory, the leading order soft photons then give no contribution to decoherence, and carry no quantum information. The sub-leading soft photons in contrast may carry finite which-path information, and the sub-leading contribution to decoherence takes an extremely simple, time-independent form depending only on the size of the interferometer. An interesting open question is whether or not dressing should also be applied at sub-leading order; we discuss the possibility of answering this question experimentally.