Timeline for Is entanglement a consequence of the uncertainty principle?
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| Jun 3, 2015 at 20:04 | comment | added | Mark Mitchison | @CuriousOne Well in the single-system case I would say that fluctuations (by which I mean the existence of states that are not eigenstates of every observable) and uncertainty (the existence of non-commuting observables) are inextricably linked. But I agree with you and the other comments that this is not actually relevant for entanglement, where the quantum fluctuations relevant for Heisenberg uncertainty happen for global observables, whereas really entanglement is about correlations between local observables. | |
| Jun 3, 2015 at 20:01 | comment | added | Mark Mitchison | @ACuriousMind I guess the point here is that the relevant fluctuations (those of the marginal/subsystem) are in fact classical, in the sense that they do not depend on the existence of non-commuting observables. So I think I am wrong to draw such a simple correspondence. Indeed the paper I linked really demonstrates that "steering" is the important feature implying entanglement, while in fact the existence of the uncertainty principle merely constrains the possible degree of non-locality. | |
| Jun 3, 2015 at 18:35 | comment | added | ACuriousMind♦ | @MarkMitchison: Entanglement is not about non-local correlations, though, just about the existence of non-simple tensors, i.e. states of a combined system which do not correspond to unique states of the subsystems. That entanglement and the uncertainty principle both imply non-locality of correlations does not mean that the uncertainty principle implies entanglement. | |
| Jun 3, 2015 at 18:14 | comment | added | CuriousOne | @MarkMitchison: Uncertainty doesn't follow from fluctuations. As Einstein is famously supposed to have said, god doesn't play dice, but that's because nature simply doesn't care to have a one-cause-one-outcome correspondence. | |
| Jun 3, 2015 at 16:40 | comment | added | Mark Mitchison | @HolgerFiedler I recommend that you read the paper that I linked. | |
| Jun 3, 2015 at 15:33 | comment | added | HolgerFiedler | It is astonishing to reed that entanglement is a consequence of Hilbert space. Entanglement happens for example when two particles get emitted together and due to conservation of parameters (momentum, spin, ...) these two particles have opposite parameters. This has nothing to do with uncertainty principle. Uncertain is which of the two particles has the one and this particle has the other parameter. | |
| Jun 3, 2015 at 15:16 | comment | added | Mark Mitchison | Yeah but the tensor product structure allows superpositions $\Rightarrow$ fluctuations $\Rightarrow$ uncertainty principle. So the physical principle underlying this purely mathematical fact is indeed linked to Heisenberg uncertainty. (It is a bit more subtle than this since the relevant fluctuations are of the marginal probability distributions, not the global state.) See, for example, the work by Oppenheim and Wehner on this topic. | |
| Jun 3, 2015 at 14:31 | history | answered | Gabriel Cozzella | CC BY-SA 3.0 |