Entanglement Distribution

Simulate distributing Bell pairs between two nodes and measure the fidelity of the resulting entangled state.

Entanglement Distribution

Distributing entanglement between distant nodes is the foundational operation of quantum networking. Unlike classical information, entanglement cannot be amplified or copied: it must be carefully generated and transmitted, with noise degrading the quality (fidelity) of the shared Bell pairs.

What Is Entanglement Distribution?

Entanglement distribution establishes a shared Bell pair between two nodes A and B:

|Φ+⟩ = (|00⟩ + |11⟩) / √2

Measuring both qubits in the same basis always gives correlated results (both 0 or both 1). This shared randomness, certified by Bell inequality violations, is the resource for QKD, teleportation, and distributed quantum computation. (The CHSH test behind that certification, including the quantity S and its classical bound of 2, is covered in the Bell inequalities lesson of the Quantum Cryptography track; in this exercise you will watch noise pull S below the quantum ideal.)

The process:

1.A source generates an entangled photon pair (via SPDC in a nonlinear crystal)
2.One photon travels to node A, the other to node B
3.Both parties detect their photons (or store them in quantum memory)
4.Heralding signals confirm both photons arrived

Depolarizing Noise

Real quantum channels introduce errors. The depolarizing channel applies a random Pauli error with probability p:

ρ \to (1 - p) ρ + \frac{p}{3} (X ρX + Y ρ Y + Z ρZ)

For a Bell pair transmitted through a depolarizing channel, the state becomes a Werner state:

ρ_{Werner} = F ∣ Φ^{+} ⟩ ⟨ Φ^{+} ∣ + \frac{1 - F}{3} (∣ Φ^{-} ⟩ ⟨ Φ^{-} ∣ + ∣ Ψ^{+} ⟩ ⟨ Ψ^{+} ∣ + ∣ Ψ^{-} ⟩ ⟨ Ψ^{-} ∣)

where the fidelity $F = 1 - p$ decreases with noise level $p$ .

Fidelity and Entanglement Quality

Fidelity measures how close the distributed state is to the ideal Bell pair:

F = ⟨ Φ^{+} ∣ ρ ∣ Φ^{+} ⟩

• $F = 1$ : perfect Bell pair
• $F < 1/2$ : state has no entanglement (below the Werner separability threshold)
• $F = 1/4$ : maximally mixed state $I /4$ (completely useless)

This is the opening of the lesson. The full walkthrough, the interactive circuit, and the graded challenge continue inside myqubit.

How this lesson works

A hands-on coding challenge. You write Qiskit-compatible Python in the browser editor, run it instantly via WebAssembly, watch the circuit and Bloch sphere react, and pass automatic output checks. The AI tutor Qubitus gives Socratic hints if you get stuck.

Part of: Quantum Networking

Build quantum networks from the ground up, entanglement distribution, quantum repeaters, the quantum internet, and satellite-based QKD.

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