Quantum teleportation and entanglement swapping
Teleportation and entanglement swapping EPR Pair is a maximally entangled two-qubit state , named after Einstein, Podolosky, and Rosen, who first pointed out these unique properties:
- Each qubit is completely random on its own (50/50 chance for 0 or 1), - Together, the pair is linked and they both collapse into the same state.
The Bell Basis are as follows:
(6)
(7)
. Pauli matrices : four important matrices that will be mentioned later on:
(8)
(9)
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(11)
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Bell State Measurement (BSM). A joint projective measurement on a Bell Pair, the outcome identifies which state the pair was in (0 or 1).
The following is a BSM acting on a two-qubit system composed of qubits XY:
(12)
Figure 1: figure of the BSM’s circuit model, the dot and circle represents the CNOT gate, while the box represents the Hadamard transform.
Teleportation Now, we will be going through the teleportation protocol [2]. Note that the names ‘Alice’ and ‘Bob’ are commonly used in both QIS and cryptography to represent the sender and receiver respectively:
1. Alice and Bob first share an EPR Pair (Arbitrary Qubits A and B). 2. Alice then takes the unknown input state (qubit X) and performs a BSM on (X+A). This yields one of four outcomes uniformly at random.
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