It is well known that superradiant decay of an ensemble of
N spins generates a complex non-classical state of light. Here, we consider the information content of a superradiant burst of photons: how is information encoded in the initial spin state distributed among the emitted photons, and can it be extracted using simple measurements? Despite the complexity of the photonic burst state, we show that a simple homodyne measurement combined with an optimized filter and linear estimator recovers the
N-scaling of the quantum Fisher information of the initial spin state (including cases exhibiting
N2 Heisenberg scaling). Even more surprising, the temporal mode with optimal information content contains a vanishing fraction of the total emitted photons in the large-
N limit, suggesting an effective compressing of information. Our results and setup represent a new way to perform cavity based readout of solid-state spin ensembles that allows one to utilize resonant spin-photon interactions.
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.