Abstract
The violation of a Bell inequality with space-like separated measurements precludes the explaination of nonlocal correlations in terms of causal influences propagating slower than light. Yet, these correlations can still be explained in a causal manner if one gives up Bell’s locality condition. Indeed, this is the explanation followed when one says something like “A measurement on the singlet state \(|\psi ^-\rangle =\frac{1}{\sqrt{2}}(|01\rangle -|10\rangle )\) yielding result ‘0’ in the computational basis of Alice prepares the state \(|1\rangle \) for Bob”. With a slightly different taste, Bohmian mechanics also provides a causal explanation for quantum correlations, which does not rely on quantum steering or collapse of the wavefunction. However, both of these explanations are much more nonlocal than a simple violation of Bell’s local causality condition implies: not only do they involve faster-than-light influences at a distance, but these influences also have immediate effects on distant particles no matter how far away they are from each other. Here we question whether such a strong violation of the notion of locality is necessary or not.
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Notes
- 1.
As a matter of fact, the same remark applies to instantaneous influences of the kind we just mentioned above.
- 2.
Note that signalling could be activated in cases where the model only produces no-signalling correlations as well. Indeed, if a marginal probability distribution can have different (no-signalling) values depending on the time chosen by some other party to perform his measurement, in the fashion of [4, 5], this change in the correlation can allow to guess the time of measurement chosen by a distant party. However we don’t consider this possibility here.
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Bancal, JD. (2014). Finite-Speed Hidden Influences. In: On the Device-Independent Approach to Quantum Physics. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-01183-7_9
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DOI: https://doi.org/10.1007/978-3-319-01183-7_9
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