  We show that Minkowskian non-local quantum field theories are not unitary. We
consider a simple one loop diagram for a scalar non-local field and show that
the imaginary part of the corresponding complex amplitude is not given by
Cutkosky rules, indeed this diagram violates the unitarity condition. We
compare this result with the case of an Euclidean non-local scalar field, that
has been shown to satisfy the Cutkosky rules, and we clearly identify the
reason of the breaking of unitarity of the Minkowskian theory.
