Quantum teleportation and entanglement swapping
3. Alice then sends the two classical bits encoding the BSM outcome to Bob. 4. Bob then applies one of the four Pauli matrices to his qubit B based on those bits and obtains the original state.
In the end, Bob ends up with a perfect copy of the original state, while Alice’s original is destroyed [2]. This was first demonstrated by the 1993 Bennet-Brassard-Crepeau-Jozsa-Peres-Wooters protocol [2]. However, this method does not work for long distances, which is where entanglement swapping comes in. Entanglement swapping Entanglement swapping – first demonstrated in the 1998 Innsbruck Experiment [4] – is a much more effective method that entangles two systems that have never interacted, enabling long-distance networks. 1. Prepare two independent Bell pairs (i.e. (A-B) and (C-D)). 2. Bring qubits B and C together and perform a BSM, the outcome of this measure determines which Pauli matrix Bob should apply. 3. As they are now conditioned, the unmeasured qubits A and D are now projected onto an entangled state – even though A and D have never interacted.
Figure 2: Principle of entanglement swapping. Two EPR sources produce two EPR Pairs (1234 is used here instead of ABCD). This results in projecting the outgoing qubits 1 (A) and 4 (D) onto an entangled state [4].
Essentially, teleportation moves a state through entanglement; swapping moves entanglement itself. While both use BSM, they achieve different outcomes. It is this combination of teleportation and swapping that enables long range quantum networks [5].
Quantum repeaters The problem . Sending a single qubit – or a photon in reality – over hundreds of kilometers is unachievable due to loss (decay).
The solution . This is where quantum repeaters come in, first proposed by Briegel, Dur, Cirac and Zoller, quantum repeaters divide the total distance into shorter segments: in each segment, qubits are entangled; entanglement swapping is then used to generate entangled links. Through this, we end up with a network of entangled qubits [5][6].
How it works . We will now dive into the linear algebra behind quantum repeaters. Suppose you have two adjacent Bell pairs ( A − 𝐵 1 and 𝐵 2 − C ) [1]:
190
Made with FlippingBook - PDF hosting