# Bell Inequality violations at large distances

Could anyone point to some references examining Bell inequality violations at large distances please?

I see many times, in pop science articles and research literature alike, that the quantum information of the entangled state is transmitted instantaneously to all components of the state. Strictly speaking, we must say that this is a theoretical prediction and provide an lower bound on the speed of information transfer from an experiment, right?

• To streamline the question and make it more answerable: may it be that you are primarily interested in the, let's call it speed of information transfer via entanglement? If you do not need to discard local hidden variables in the same experiment, maybe you don't actually need Bell inequalities in the same question? – agaitaarino May 27 '18 at 5:51

I think there is a conceptual thing going on here that needs clarifying (I'll leave the experimental links to others). I presume the question is predicated on the idea that, well, measurements are made within a certain time of each other, which is compared to the distance between the places where the measurements are being made. The concern is that this only gives a bound: if information is transmitted, it happens faster than some velocity which we have now bounded.

However, what one ought to do is consider what special relativity tells you: if two events are space-like separated, there is no notion of temporal ordering. Different observers, travelling at different velocities, can see the events happening in different orders (or simultaneously). So, all you need to know is that the measurement events are space-like separated (i.e. the distance between the events is larger than speed of light $\times$ time between events), and that is enough.

Also, there's a terminology issue. Bell tests do not talk about the transmission of information, but the presence of correlation. The term information would suggest that one party can choose some information to communicate to another party. This cannot happen faster than the speed of light. But the "random decision" made when a measurement is made on an entangled state is somehow resolved everywhere simultaneously, but does not communicate any information.

• Thank you for these clarifications. I mostly agree. But if we take quantum information to mean "the information needed to specify a quantum state", then this information does travel faster than light. The results of the measurement are reflected in the state of the distant qubit. You are right that doesn't allow faster that light communication. – psitae May 28 '18 at 12:49
• At some point, one is getting into a dangerous world of semantics/interpretation. I was mostly trying to counsel that I think the word information is a bad one to use in this context because its default usage has too many connotations that might be falsely inferred. Even talking about "this information does travel faster than light" makes dangerous intimations. It seems like one is saying something is travelling from A to B, but actually, some obervers would say that it is travelling from B to A (or backwards in time). All very murky territory. – DaftWullie May 28 '18 at 14:04

The largest scale Bell test done thus far is the "Cosmic Bell Test" of 2017. It ruled out hidden variables within a distance of 600 light years from Earth.

The 16 significant Bell test experiments performed between 1972 and 2018 are listed here with references to the original papers.

• The huge distance in the cosmic bell test was the distance between the sources of randomness. I think the asker cares about the distance between the actual measurements. – Craig Gidney May 28 '18 at 1:39
• @CraigGidney: I thought that was possible too, so I have given the list of all 16 experiments that I think are worth looking at, in case if the user would like to know the answer to the latter question. – user1271772 May 28 '18 at 2:34