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Starting with two qubits $|00>$, I can obtain a bell state by applying a Hadamard gate and then a CNOT gate [ref].

The two qubits in a bell state are entangled. It is a common part of giving the following illustration when entanglement is introduced as a concept:

If Bob and Alice take one of the entangled qubits each, isolate them to avoid collapse, and then travel far away from each other (even thousands of kilometers), then when Alice measures her qubit, Bob's qubit also will collapse to the same state when measured.

Initially the two qubits must have been spatially close so that the operations could be applied on them that cause them to entangle.

My question is: How practical is it to then isolate the two qubits without collapsing them? We were told that many physical phenomena (photon polarization; electron spin) can model a qubit. Is there any physical phenomena where there already is appratus which can isolate and spatially separate qubits after entanglement?

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    $\begingroup$ Of course, Bell states are regularly made. For example, if the constituent particles are photons, they usually fly out of the apparatus that makes them in different directions. So you don't need to do anything to spatially separate them. $\endgroup$ – knzhou Jan 16 '20 at 19:04
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    $\begingroup$ What's "of course" about that? How could you have photons as qubits (and hence, a stable model of computation) if they are flying out of the apparatus? $\endgroup$ – Peeyush Kushwaha Jan 16 '20 at 22:25
  • $\begingroup$ I just meant "qubit" in the sense of any two-state system. If you're asking about practical quantum computers, then it depends very much on the particular computer. $\endgroup$ – knzhou Jan 16 '20 at 22:37
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In a photonics context, a standard method to generate entangled photons is SPDC. This generates a pair of photons whose polarisation are entangled. This is "practical" enough to be standard in quantum optics laboratories. Note that the direction in which the photons are emitted can be controlled, and thus the photons used for whatever protocol one is trying to implement.

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  • $\begingroup$ This is pretty interesting. A follow up question: Is it possible to prevent "measurement" (which collapses the superposed state) while the photons are in the apparatus? $\endgroup$ – Peeyush Kushwaha Jan 19 '20 at 12:41
  • $\begingroup$ @PeeyushKushwaha which apparatus? The collapse happens when the system is measured by something (be it due to the measurement apparatus or environmental noise) $\endgroup$ – glS Jan 20 '20 at 9:25
  • $\begingroup$ Let me re-formulate the question: Is it possible to prevent the collapse after the entangled photons are emitted? Or they are bound to collapse, perhaps as soon as they leave / hit boundaries of apparatus in quantum optics labs which was being used to conduct the experiment? $\endgroup$ – Peeyush Kushwaha Jan 22 '20 at 5:15
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    $\begingroup$ Collapse happens upon measurement or other types of (wanted or not) interaction. Two entangled photons travelling in a vacuum will remain entangled indefinitely, in principle. Even in practice, entangled photons can be transmitted with pretty good fidelity over large distances (several kilometres) using fibre-optic cables $\endgroup$ – glS Jan 22 '20 at 11:46
  • $\begingroup$ I hadn't understood what you were saying at the time. Now I do. Can you include more information in your answer about using fibre-optic cables to transmit these entangled photons and manifestation of quantum protocols several KM apart? $\endgroup$ – Peeyush Kushwaha Oct 18 '20 at 22:08

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