Entanglement Swapping

In the previous chapter, we found that entanglement is a rather strange quantum phenomenon with many counterintuitive notions. Here is an example that sets up an entangled state for two qubits that are always far apart and have no direct interaction with each other! No matter how strange it seems, this kind of entanglement is useful in several quantum cryptographic protocols.

We start with four qubits: $A$, $B$, $C$, and $D$. Qubits $A$ and $B$ are prepared in an entangled state while $C$ and $D$ are also prepared in an entangled state but one that is completely independent of the $AB$ entangled state. The qubits go off in different directions as shown in the image below. We then arrange to carry out a measurement on qubits $C$ and $D$. With the right choice of measurement basis states, we find that qubits $A$ and $D$ end up in an entangled state even though they have never met up with each other and have not interacted directly. We say that the procedure has swapped the entanglement from the $AB$ and $CD$ systems for entanglement in the $AD$ system.