Nonlocality proven by tuning the phase of an undetected noncommutative fourth photon

 https://www.nature.com/articles/s41467-023-37228-y#citeas

 This is nonlocality, the basis of the Nobel Prize in 2022. I recommend Professor Tim Maudlin's recent youtube talk on Bell's nonlocality experiment to understand this. "This second-order interference of the entangled state can not be explained by local hidden variable theory and is considered non-local. In this setting, any mutual influence between the two observations is excluded under strict Einstein locality conditions7. This phenomenon, predicted by quantum physics, cannot be accounted for by any local theory and represents one of the most profound foundational insights in physics8." So if you realize that nonlocality arises from noncommutativity then entanglement is not first required. "In almost all scenarios in which non-local interference is observed, entanglement—or more generally some form of quantum correlation—is the basic ingredient. In this work, we show that this is not necessarily the case, and demonstrate multiphoton non-local quantum interference, which does not need entanglement....Then we go beyond and demonstrate a surprising physical property: We observe non-local quantum interference that does not require quantum entanglement. Specifically, we tune the phase of a photon that we never detect, and observe interference with the rest photons....However, here no quantum entanglement between any properties of the photons exists, but one can observe interference with the mere existence of a multi-photon state. It arrives from a coherent superposition of the origin of the multi-photon state.....In this case, we can detect and observe three-photon interference by tuning the phase of the fourth photon, which is undetected. This finding shows the effect that one has non-local quantum interference that does not require entangled states....This effect occurs not because of a superposition of the photons’ external properties, such as path, polarization, and so on. Instead, it happens because of a fundamental unknowability where the photons have been generated. This underlying principle allows us to show how we can manipulate the interference of three photons by introducing a phase in the fourth photon that we never detect....We tune the phase of a photon that we never detect, and observe interference of the rest photons. Multiphoton interference appears when the coincidence measurements of only partial interfering photons are performed....Our experiment thereby demonstrates in a direct way how the lack of knowledge about a quantum system can lead to multiphoton non-local quantum interference, a feature that cannot solely be described by entanglement.....Qian, K., Wang, K., Chen, L. et al. Multiphoton non-local quantum interference controlled by an undetected photon. Nat Commun 14, 1480 (2023).