Quantum gate description for induced coherence without induced emission and related phenomena

TL;DR

This paper develops quantum gate models for photon pair creation and path alignment in nonlinear crystals, enabling a unified description of induced coherence phenomena and related quantum experiments.

Contribution

It introduces unitary quantum gates for photon pair creation and path alignment, providing a new framework for analyzing induced coherence without induced emission.

Findings

Quantum circuits for photon pair generation and Bell states

Effective nonunitary description of nonlinear crystals in experiments

Modular creation of quantum state superpositions

Abstract

We introduce unitary quantum gates for photon pair creation in spontaneous parametric down-conversion nonlinear crystals (NLs) and for photon path alignment. These are the two key ingredients for the method of "induced coherence without induced emission" and many ensuing variations thereof. The difficulty in doing so stems from an apparent mixing of the mode picture (such as the polarization of photons) and the Fock picture (such as the existence of the photons). We illustrate utility of these gates by obtaining quantum circuits for the experimental setups of the frustrated generation of photon pairs, identification of a point-like object with undetected photons, and creation of a Bell state. We also introduce an effective nonunitary description for the action of NLs in experiments where all the NLs are pumped coherently. As an example, by using this simplifying picture, we show how NLs can be used to create superposition of given quantum states in a modular fashion.