I have a question regarding quantum teleportation. The scenario is the usual one where Alice as a qubit to transmit, A, and shares an entangled pair of qubits {B1,B2} with Bob. My question is: once Alice performs the Bell measurement on {A,B1}, isn't the entanglement between B1 and B2 destroyed? If it's true, how can it be restored? Because thinking about a real case scenario it doesn't look like it's desirable to destroy the entanglement of the qubits used for teleportation.
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$\begingroup$ you are correct in that you can only use the entangled state once. You can think of it as a resource you have to "spend" to achieve the state transfer. It is indeed a "one-use-only" resource. If you want to send multiples states via teleportation, you need multiple entangled states $\endgroup$– glSCommented Nov 8, 2022 at 13:01
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Once you measure the state collapses and the entanglement is lost. Note that measurements are irreversible, and therefore this is just the price you pay.
If you could maintain the entanglement permanently while performing multiple measurements you could transmit information faster than light by repeating the measurement on B2 while changing the state of B1!
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$\begingroup$ Thanks for the answer. But I don't understand then how this is handled in the real world. Like if I set two systems so that they share an entangled pair, then when they are distant I use one system to teleport a qubit to the other one, once I've lost the entanglement how can I reuse those systems again for teleportation? Does a "re-entanglement at distance" operation exist? Because otherwise it looks like whatever devices I set for quantum communication they are basically a throwaway. $\endgroup$– marcoCommented Nov 7, 2022 at 13:14
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$\begingroup$ To entangle two systems they have to either directly interact, or alternatively you could do an entanglement swapping if there is some reason why you cannot have B1 and B2 ever interacting again, but then you might as well use whatever you used to do the entanglement swap to perform the teleportation instead! $\endgroup$– peepCommented Nov 7, 2022 at 13:17
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$\begingroup$ This is determined by the statistics. One sees the correlation/entanglement only in approx. 25% of the comparisons of the measurements. This is because the measuring device destroys the state of the particle (e.g. the orientation of its electric field component) and, in addition, you only get a result at all in about 50% (for Bob and Alice separately and different in time). But it gives us the certainty that we have entangled particles. … $\endgroup$ Commented Nov 8, 2022 at 4:58
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$\begingroup$ … If this seems too complicated for you, just assume that the entangled states of the particles are unambiguous after generation, but that we only detect these correlated states statistically correctly in about 25% of cases. If someone from the outside interferes, intercepts the particle and replaces it, then the statistics fall far below 25% and the attacker is unmasked. $\endgroup$ Commented Nov 8, 2022 at 4:58