Does the speed of quantum entanglement exceed the speed of light?

Too long; didn’t read version:

“Spooky action at a distance (superluminal)” is an outdated view. According to special relativity, there is no interaction between events at spacelike separation. The mainstream view in academia is to consider quantum states and measurement bases together as reality, known as contextuality. Nonlocality is a corollary of contextuality.

Body:

Discussing the “speed” of quantum entanglement is meaningless.

If the distance between two measurement events a and b is spacelike, then a is neither in the past nor in the future of b.

This is because, in special relativity, if the distance between a and b is spacelike, whether a is in the past or future of b depends on the observer’s frame of reference. Therefore, there is no definite time sequence between a and b, and thus no causal relationship.

In this case, we should say: the measurement results of a and b exhibit nonlocal correlations, rather than saying that the measurement result of a affects the measurement result of b, or vice versa.

See the diagram below:

In the above diagram, the two events a and b are outside each other’s light cone, so there is no interaction between them. What really exists is the correlation between their measurement results.

Correlation is not hard to understand because they both originate from a Bell pair.

What is truly difficult to understand is: when you change the measurement basis (refer to various Bell test experiments), you will find that this correlation also depends on the measurement basis, i.e., it changes with the measurement basis. This leads to at least one of the following conclusions:

1. The quantum state $|\psi\rangle$ itself is incomplete and cannot fully describe reality. Only when the measurement basis $\mathsf{E}$ is determined, $(|\psi\rangle,\mathsf{E})$ is complete. This is called contextuality, meaning reality only exists when the measurement basis is determined, and does not exist before that. In this case, nonlocality is a corollary of contextuality.

2. If you insist that local and non-contextual reality exists and propose a local and non-contextual hidden variable theory, then you must accept negative probabilities in this theory. In this case, your theory cannot be described by classical probability theory but must use non-Kolmogorov probability theory.

3. If you believe that negative probabilities themselves violate reality, then refer back to the first point.

The contextuality mentioned in the first point is currently mainstream in academia. There are more and more papers studying contextuality, which should be considered a small trend in quantum information research.

The core idea of contextuality is: quantum reality only exists when the measuring instrument is given. Some people also call this sub-reality or contextual reality. Therefore, I personally think that the translation of contextuality is not very good and should be called “context dependence.” The “context” here refers to the measuring instrument.

Unfortunately, a significant number of scholars still do not understand contextuality, and it is not introduced in most standard textbooks, let alone in popular science and mass culture. But this is understandable: contextuality was proposed in the 1990s, 30 years later than Bell’s theorem, and is somewhat at the forefront of academia.

In summary: “spooky action at a distance (superluminal)” is an outdated view. According to special relativity, there is no interaction between events at spacelike separation. The mainstream view in academia is to consider quantum states and measurement bases together as reality, known as contextuality. Nonlocality is a corollary of contextuality.

References

1. Entropy 2021, 23(12), 1660 https://doi.org/10.3390/e23121660