Nonlocality of single quanta

Abstract

Although regarded today as an important resource in quantum information, nonlocality has yielded over the years many conceptual conundrums. Among the latter are nonlocal aspects of single particles which have been of major interest. In this paper, the nonlocality of single quanta is proved using a delayed choice modification of the complex-valued weak values in a square nested Mach--Zehnder interferometer with spatially separated measuring devices. We show that local hidden variables models may use hidden signaling and a list of contextual instructions to replicate quantum probabilities and the mean pointer shifts corresponding to the measured real part of weak values, but in doing so necessarily fail to reproduce the quantum variance of pointer shifts. Our analysis also demonstrates that the recently proposed weak values of quantum histories are inherently nonlocal physical quantities due to their dependence on the total Feynman sum that yields the complex-valued quantum probability amplitude for the studied quantum transition.