A quantum state of light has been successfully teleported through more than 30 kilometers (around 18 miles) of fiber optic cable amid a torrent of internet traffic – a feat of engineering once considered impossible.
the bell pair, |β₀₀>, which consists of /two/ entangled photons "P1" and "P2".
First, I make a bell pair (P1,P2), and apply some quantum operation interacting P1 with |ψ>. Then I measure P1 and |ψ>, which will give me two bits of information "M1","M2". I send to my friend over the optical fibre: the photon P2 (quantum), and M1,M2 (classical). Then, they can apply some operations which are decided by M1,M2 onto P2 and they will get back the original state |ψ>.
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there is an analogy to RSA (if you're familiar), where the shared bell state is kind of like the key pair, encryption corresponds to combining the original state and measuring, and decrypting corresponds to applying the operations to the other half of the bell pair.
The advantage here, over sending the initial state |ψ> directly over the optical fibre, is that the bell state can be established by e.g. a third node sending half of a bell pair to each party, so that we only need to communicate classically to achieve quantum teleportation.
But also, quantum teleportation is a means of moving quantum states between different /types/ of qubit - of which there are many, which are good for different things.
close! Let me give some more detail.
There are 3 "objects" to consider here
First, I make a bell pair (P1,P2), and apply some quantum operation interacting P1 with |ψ>. Then I measure P1 and |ψ>, which will give me two bits of information "M1","M2". I send to my friend over the optical fibre: the photon P2 (quantum), and M1,M2 (classical). Then, they can apply some operations which are decided by M1,M2 onto P2 and they will get back the original state |ψ>.
there is an analogy to RSA (if you're familiar), where the shared bell state is kind of like the key pair, encryption corresponds to combining the original state and measuring, and decrypting corresponds to applying the operations to the other half of the bell pair.
The advantage here, over sending the initial state |ψ> directly over the optical fibre, is that the bell state can be established by e.g. a third node sending half of a bell pair to each party, so that we only need to communicate classically to achieve quantum teleportation.
But also, quantum teleportation is a means of moving quantum states between different /types/ of qubit - of which there are many, which are good for different things.
I understand like 25% of this but thank you for trying.