Quantum teleportation and entanglement swapping
- Link 1:
- Link 2:
Together, their joint state is as follows.
|Φ+ ⟩ AB 1 ⊗ |Φ+ ⟩ B 2 C
(13)
Here, node B holds qubits 𝐵 1 and 𝐵 2 , while nodes A and C are the endpoints we want to entangle. Next, a BSM is performed on 𝐵 1 𝐵 2 .
(14)
Interpretation and explanation:
- The BSM projects 𝐵 1 𝐵 2 onto one of the |Bell ab ⟩ states (Probability 1/4)
- Conditioned on outcome ( a,b ), the endpoints A and C are left in:
(15)
- Here, X a Z b are Pauli ‘frame’ corrections, where:
(16)
- Now, we send (a,b) through classical means, then at node C , we apply Z b X a to restore the link between |Φ + ⟩ AC
- We can see how no qubit has ever traversed B , only correlation.
For multiple links (i.e. A − B, B − C, C − D you start with:
(17)
1.
BSM is performed on 𝐵 1 𝐵 2 → entanglement between A and 𝐶 1 up to Pauli Frame
2. BSM is then performed on 𝐶 1 𝐶 2 → entanglement between A and D up to the accumulated frame.
(18)
Then, apply the accumulated frame and the final pair is brought back to |Φ + ⟩
AD . Through this, we can see
how no qubits – but classical bits –are transferred the full distance (the Pauli matrices).
Where are we at now? What has been shown? Quantum teleportation : The first demonstration of quantum teleportation was done through photonic teleportation in the Zeilinger Group. This was done by Bouwmeester et al. (1997). [3]
Entanglement swapping : The first experimental proof that a Bell State Measure can entangle distant, unrelated systems that have never previously interacted. This was done by Pan et al. (1998). [4]
191
Made with FlippingBook - PDF hosting