In learning device-independent QM from [https://arxiv.org/abs/1303.3081], Scarani tells us that all quantum statistics involving one particle can be reproduced with local (hidden) variables. He then constructs the statistics of a qubit in such a model. Insightful as this is, it is still not clear to me why all single-particle statistics can be reproduced. Is it because the local variable can hold information about the single-particle state? Why can't it do the same in a many-particle system?

  • $\begingroup$ Here's what I suppose now: In the single-particle case, the local variable could know exactly what probability distribution to present so it is impossible to determine whether or not the source is classical or quantum. In the many-particle case, we see correlations that cannot be explained in this way because we must allow each particle to be treated as a black-box. Almost inherently this implies that LV's cannot produce the statistics due to entanglement without assuming that the LV's are communicating. Is this correct? $\endgroup$ – PhysMath Jun 20 at 21:17

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