Entanglement Swapping Simulation

Entanglement Swapping Simulation

Entanglement swapping extends entanglement across nodes without transmitting qubits the full distance. It is the fundamental operation of quantum repeaters. Implementing it in simulation builds concrete intuition for how the Bell state measurement works and why the correction operations restore the target state.

The Protocol in Detail

The 4-qubit initial state is:

|Φ+⟩₁₂ ⊗ |Φ+⟩₃₄

Node B's goal: measure qubits 2 and 3 in the Bell basis to create entanglement between qubits 1 and 4 (A and C).

Bell Basis Measurement

The two classical bits (m2, m3) from this measurement indicate which of the four Bell states was measured.

Correction Operations

After correction, qubits 1 and 4 are in state |Φ+⟩: entangled even though they never interacted.

Why This Works

The four-qubit initial state can be rewritten in the Bell basis of qubits 2 and 3:

|Φ+⟩₁₂ ⊗ |Φ+⟩₃₄ = (1/2) Σ_{m2,m3} |Bell_{m2,m3}⟩₂₃ ⊗ (correction) |Φ+⟩₁₄

When B measures in the Bell basis and gets outcome (m2, m3), qubits 1 and 4 collapse to the state (correction) |Φ+⟩: a Bell pair with a known (and correctable) Pauli rotation. After A applies the correction, A and C share a perfect |Φ+⟩.

Your Challenge

The starter code provides the 4-qubit initial state and utility functions. Implement bell_basis_measurement (the BSM on qubits 2 and 3) and apply_correction (the correction on qubit 1 based on the measurement result).