  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 studied in a
square nested Mach-Zehnder interferometer with spatially separated detectors
using a delayed choice modification of quantum measurement outcomes that depend
on the complex-valued weak values. We show that if spacelike separated Bob and
Alice are allowed to freely control their quantum devices, the geometry of the
setup constrains the local hidden variables models. In particular, hidden
signaling and a list of contextual instructions are required to split a quantum
state characterized by a positive Wigner function into two quantum states with
non-positive Wigner functions. This implies that local hidden variables models
could rely neither on only two hidden variables for position and momentum, nor
on simultaneous factorizability of both the hidden probability densities and
weights of splitting to reproduce the correct quantum distributions. While our
analysis does not fully exclude the existence of nonfactorizable local hidden
variables models, it demonstrates that the recently proposed weak values of
quantum histories necessitate contextual splitting of prior commitments to
measurement outcomes, due to functional dependence on the total Feynman sum
that yields the complex-valued quantum probability amplitude for the studied
quantum transition. This analysis also highlights the quantum nature of weak
measurements.
