Single-particle entanglement gives rise to truly nonlocal effects like single-particle steering

Abstract: In 1927, at the Solvay conference, Einstein posed a thought experiment with the primary intention of showing the incompleteness of quantum mechanics; to prove it, he uses the instantaneous nonlocal effects caused by the collapse of the wave function of a single particle -the spooky action at a distance-, when a measurement is done. This historical event precede the well-know Einstein-Podolsk-Rosen criticism over the incompleteness of quantum mechanics. Here, by using the Stern-Gerlach experiment (SGE), we demonstrate how the instantaneous nonlocal feature of the collapse of the wave function together with the single-particle entanglement can be used to produce the nonlocal effect of steering. In the steering process Bob gets a quantum state depending on which observable Alice decides to measure. To accomplish this, we fully exploit the spreading (over large distances) of the entangled wave function of the single-particle. In particular, we demonstrate that the nonlocality of the single-particle entanglement allows the particle to know which detector Alice is using to steer Bob's state. Therefore, notwithstanding strong counterarguments, we prove that the single-particle entanglement gives rise to truly nonlocal effects at two far a away places. This open the possibility of using the single-particle entanglement for implementing truly nonlocal task.