Project: Entanglement Network

A quantum network's job is to share entanglement between distant nodes — and to make that entanglement good enough despite lossy channels. This capstone wires the two core primitives: distribution of Bell pairs across a four-qubit, two-node network, and the bilateral-CNOT step that begins entanglement purification.

Distributing Bell pairs

Each link in the network shares a Bell pair $|\Phi^+\rangle = \tfrac{1}{\sqrt 2}(|00\rangle + |11\rangle)$, one half at each node, created by H then CX. Our toy network has two such pairs:

with Alice holding qubits $0, 2$ and Bob holding $1, 3$. After distribution the joint state is the product $|\Phi^+\rangle_{01} \otimes |\Phi^+\rangle_{23}$.

Why purification is needed

Real channels degrade a Bell pair into a mixed state of fidelity $F < 1$ to $|\Phi^+\rangle$. Purification (Bennett et al., 1996; the BBPSSW protocol) consumes two imperfect pairs to distill one pair of higher fidelity. The opening move is a bilateral CNOT: each node applies a local CNOT from its half of the kept pair onto its half of the sacrificial pair,

Both operations are strictly local — no quantum communication is required beyond the pre-shared pairs — which is what makes purification practical over long distances.

Reading out the distillation

After the bilateral CNOT, both parties measure the sacrificial pair (qubits $2, 3$) in the computational basis and compare results over a classical channel. Coincident outcomes "pass" and herald a kept pair of improved fidelity; mismatches are discarded. Iterating the protocol drives the kept-pair fidelity toward $1$, the resource a repeater chain needs to extend entanglement across the whole network.

Try it

Distribute the two Bell pairs and apply the bilateral CNOT. The grader checks the 4-qubit statevector right after the local CNOTs — the state from which the heralding measurement is made.

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