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EPR pairs are used in superdense coding and quantum teleportation, but these protocols assume that Alice & Bob "share" half of an entangled quantum state.

How does this "sharing" initially happen?

Can you establish an EPR pair between Alice & Bob, without prior entanglement, using only classical (non-quantum) communication? Alice & Bob have access to quantum bits locally but cannot pass quantum bits between one another.

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No, it is not possible to entangle two qubits using only classical communication, more generally, LOCC can not create entanglement.

One can create a shared Bell pair, for example, if Alice makes two qubits interact and then physically ships one of them to Bob. If you're thinking "duh, what's the point of superdense coding then?" imagine creating an entangled pair today and sending a 2-bit message one year later (and either way, from A to B or from B to A). Now it makes sense, right?

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    $\begingroup$ Thank you, this was helpful for understanding. Accepted as the answer. $\endgroup$
    – Joseph Briones
    Commented Jul 17, 2022 at 20:52
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There are only two ways to create EPR pairs distributed between spacelike separated Alice and Bob: use a quantum channel or distill EPR pairs from pre-existing entangled states. In other words, local quantum operations and classical communication are insufficient to create new entanglement.

However, the vacuum state of any relativistic quantum field theory, such as QED, is entangled and may be used as pre-existing entanglement for the purpose of distilling EPR pairs. See this paper.

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  • $\begingroup$ Very cool ref! Although I wonder if this protocol can tolerate anyone in the universe sneezing during its execution. $\endgroup$
    – Nikita Nemkov
    Commented Jul 17, 2022 at 22:16
  • $\begingroup$ A sneeze sufficiently far away is probably fine. After all, there are range limits in the basic protocol which you can view either as an exchange of virtual photons or as an interaction with a single coherent quantum fluctuation extending over the spacelike separation between Alice and Bob. Either view reveals that the protocol is range-limited. The variant with Alice and Bob on accelerated trajectories does extend the range, but it seems that acceleration might also protect Alice's and Bob's entanglement harvesters from Charlie's sneeze! $\endgroup$
    – Adam Zalcman
    Commented Jul 18, 2022 at 0:02
  • $\begingroup$ Thank you for the helpful reply & reference. What would be considered a quantum channel in this case? If Alice and Bob were physically connected by a superconducting wire as in paper, university press? $\endgroup$
    – Joseph Briones
    Commented Jul 18, 2022 at 17:01

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