The time-frequency degree of freedom of the electromagnetic field is the final frontier for single-photon measurements. The temporal and spectral distribution a measurement retrodicts (that is, the state it projects onto) is determined by the detector's intrinsic resonance structure. In this paper, we construct ideal and more realistic positive operator-valued measures (POVMs) that project onto arbitrary single-photon wavepackets with high efficiency and low noise. We discuss applications to super-resolved measurements and quantum communication. In doing so we will give a fully quantum description of the entire photo detection process, give prescriptions for (in principle) performing single-shot Heisenberg-limited time-frequency measurements of single photons, and discuss fundamental limits and trade-offs inherent to single-photon detection.
@article{arxiv.2005.11305,
title = {How to Project onto an Arbitrary Single-Photon Wavepacket},
author = {Tzula B. Propp and Steven J. van Enk},
journal= {arXiv preprint arXiv:2005.11305},
year = {2020}
}