Entanglement Swapping

Demonstration of Entanglement Purification and Swapping Protocol to Design Quantum Repeater in IBM Quantum Computer

Consider entanglement swapping between two repeater stations. This consideration requires 3 parties; Alice, Bob and Charlie.

Consider the setup as: Alice -> Charlie -> Bob

Charlie is the intermediary repeater station between Alice and Bob. Swapping happens at Charlie.

There are two entangling pairs of qubits: A0 - C0 and B0 - C1; where:

A0 = Alice
B0 = Bob
C0 = Charlie
C1 = Charlie

Entanglement production: produces pairs; A0 - C0 and B0 - C1.

Each entanglement pair was entangled by the Bell-state $\ket{\psi^+} = \frac{1}{\sqrt{2}} (\ket{00} + \ket{11})$

Initially, A0 and C0 are entagled (Alice and Charlie) ; B0 and C1 are entangled (Charlie and Bob).

After swapping, Alice A0, and Bob B0, get entangled. Charlie's C0 and C1 get entangled. Therefore, Alice and Bob get entangled, and Charlie's two initially unrelated qubits also get entangled.

Design of a Quantum-Repeater using Quantum Circuits and Benchmarking Its Performance on an IBM Quantum Computer

Consider two Bell pairs: $\ket{\Phi^+}{12}$ and $\ket{\Phi^+}{34}$; where $1, 2, 3, 4$ represents the locations of the qubits.

$1$ represents Alice's node.

$2$ and $3$ represents the nodes at the quantum repeater.

$4$ represents Bob's end node.

Performing Bell State Measurement between qubits in $2$ and $3$, projects the qubits in $1$ and $4$ into the entangled state $\ket{\Phi^+}_{14}$ up to a Pauli correction operation ${I, Z, X, Y}$ that depends on the BSM result.

Results of the BSM are sent to Bob via a classical channel (Teleportation protocol). The correction operation is the performed by Bob. Thus entanglement has been successfully teleported between Alice and Bob.