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This is a very basic question. Consider an entangled pair |00> + |11> of two qubits $q_1$ and $q_2$. Now, we measure $q_1$ and its outcome is 0. I know that $q_2$'s state "collapses" to 0 instantly. I have some confusion regarding this.

How has this "collapse" of $q_2$'s state been verified? By "observing" (equivalent to "measuring"?) it?

Or is there a way to tell that a qubit is no long as superposition to two states -- without actually observing/measuring it?

Thanks.

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First you cannot tell if the entangled partner has been measured, this would lead to faster than light signaling which should not be allowed by relativity.

Secondly, if you only measure both qubits in the $|0\rangle,|1\rangle$ basis you cannot say anything about entanglement. The particles could be also in a mixed state.

In order to truly test that there is some weird quantum phenomena going on you need many ensembles of the pair of entangled particles and measure in a least three different bases. For flying photons or electrons this can be achieved by just rotating the angle of one of the polarization measuring devices. See Bell test for more information. If the measured correlations between the different bases violate Bell's inequality (as entangled particles do), it leads to the conclusion that some of the following are true: devices are able to modify hidden parameters that are not localized with the particles (nonlocality), particles do not have defined quantities until one of them is measured (nonrealism), the devices are always highly correlated with the particles in order to reproduce the results of quantum mechanics (superdeterminism).

In Copenhagen interpretation, we just say the particles follow Schrödinger equation until you measure one of the entangled particles, in that moment you collapse the state of both. This reproduces very well the experimental results.

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There's no way to check if the state has collapsed or not. That would allow you to, for example, distinguish collapse interpretations from many worlds interpretations. Even just within collapse interpretations, it would allow you to signal faster than light or else find a preferred inertial frame for the universe. That's impossible by the no signalling theorem.

What you can check is how the measurements at both ends relate, and whether this relationship depends on the order of the measurements (it doesn't).

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  • $\begingroup$ Thanks. How does relating the measurement outcomes (irrespective of the order) confirm that the qubits were entangled? They could very well be in a mixed state of 00 and 11. I guess I'm fundamentally trying to understand how the entanglement-magic was verified (was it, convincingly?). $\endgroup$
    – Brian
    Feb 20, 2023 at 0:51
  • $\begingroup$ @Brian The strictest test for entanglement is to violate bell inequalities. $\endgroup$ Feb 20, 2023 at 4:16
  • $\begingroup$ @Brian for example arxiv.org/abs/1212.0533 $\endgroup$ Feb 20, 2023 at 4:37
  • $\begingroup$ Thanks. I'm reading up more on Bell's Theorem/inequality to get a handle on above. One last question: Do we know for sure that $q_2$'s state "collapses" or are we just guessing it to be the case based on experiments? Whats the current knowledge in this regard? Thanks. $\endgroup$
    – Brian
    Feb 20, 2023 at 22:27

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