The Hong–Ou–Mandel experiment: from photon indistinguishability to continuous-variable quantum computing

Abstract

Abstract We extensively discuss the Hong–Ou–Mandel experiment by taking an original phase-space-based perspective. For this, we analyze time and frequency variables as quantum continuous variables in perfect analogy with position and momentum of massive particles or with the electromagnetic field’s quadratures. We discuss how this experiment can be used to directly measure the time-frequency Wigner function and implement logical gates in these variables. We also briefly discuss the quantum/classical aspects of this experiment providing a general expression for intensity correlations that make explicit the differences between a classical Hong–Ou–Mandel-like dip and a quantum one. Throughout the manuscript, we will often focus and refer to a particular system based on AlGaAs waveguides emitting photon pairs via spontaneous parametric down conversion, but our results can be extended to other analogous experimental systems and to various degrees of freedom. Graphical Abstract The Hong–Ou–Mandel experiment is a landmark in quantum optics, showing the bunching of indistinguishable bunch. In the present contribution, we give another perspective to this experiment based on a phase space representation of the continuous degrees of freedom of the single photons sent into the input arms of such interferometer. We show that the coincidence detection in the output ports of an Hong– Ou–Mandel interferometer is a direct measurement of the Wigner function of the produced photons in a given region of space, and we discuss how continuous degrees of freedom of single photons can be used in continuous variables quantum protocols, as quantum error correction and metrology. Our results open the perspective of broadening even more the applications of single photon-based quantum information-related protocols.