How do photonic Bell measurements work?

Entangling Bell measurements are an essential ingredient in many photonic quantum technologies. In optical quantum computing they are employed as fusion gates to create edges in graph states, while in quantum communications protocols they may be used to implement entanglement swapping in quantum repeater networks (entanglement distribution networks) for extending the range of entanglement links. In this post I’ll describe how this very simple optical circuit works and address some of the nuances and common misconceptions surrounding it. What is a Bell measurement? A Bell measurement is a two-qubit operation that projects onto the maximally-entangled Bell basis comprising the four…