Entanglement Swapping

Entanglement Swapping

Entanglement swapping lets two parties (Alice and Bob) become entangled even though they never directly interacted. A relay (Charlie) does a Bell measurement on his two qubits, one entangled with Alice, one with Bob. This is the core operation inside every quantum repeater, a device you will meet later in this track, and in this challenge you build it from four qubits.

Teleportation in Disguise

You already know quantum teleportation: a Bell measurement plus two classical bits moves an unknown qubit state from one place to another. Entanglement swapping is exactly teleportation where the "unknown state" happens to be half of another Bell pair. Charlie teleports his Alice-side qubit into Bob's pair, and the entanglement comes along for the ride. Nothing about teleportation required the input to be a standalone qubit, and swapping is the payoff for that generality.

The Protocol

Reading the Outcome

Charlie's Bell measurement has four outcomes, and each projects Alice and Bob into a different Bell state. In the Z basis only the parity matters: Charlie's CNOT-target outcome (qubit 2) is the parity bit that names the family.

Charlie's other outcome (qubit 1, the phase bit) distinguishes + from − within each family, which is invisible to Z-basis measurements. The measurement keys follow Qiskit's convention, qubit 0 is the rightmost character, so a key reads [Bob][Charlie_R][Charlie_L][Alice], and the verification code checks every shot against the parity rule above: 100% of outcomes must be consistent, something that cannot happen unless your two TODO steps genuinely entangled Alice with Bob. Remember from Density Matrices and Mixed States that either half of a Bell pair on its own is maximally mixed, so Alice's marginal statistics stay 50/50 no matter what and the swap shows up only in the joint counts.