  Lattice quantum chromodynamics (QCD) provides the only known systematic,
nonperturbative method for first-principles calculations of nucleon structure.
However, for quantities such as lightfront parton distribution functions (PDFs)
and generalized parton distributions (GPDs), the restriction to Euclidean time
prevents direct calculation of the desired observable. Recently, progress has
been made in relating these quantities to matrix elements of spatially
nonlocal, zero-time operators, referred to as quasidistributions. Even for
these time-independent matrix elements, potential subtleties have been
identified in the role of the Euclidean signature. In this work, we investigate
the analytic behavior of spatially non-local correlation functions and
demonstrate that the matrix elements obtained from Euclidean lattice QCD are
identical to those obtained using the LSZ reduction formula in Minkowski space.
After arguing the equivalence on general grounds, we also show that it holds in
a perturbative calculation, where special care is needed to identify the
lattice prediction. Finally we present a proof of the uniqueness of the matrix
elements obtained from Minkowski and Euclidean correlation functions to all
order in perturbation theory.
