A crucial requirement is that the states of single particle have positive energy.
It has been used to support the conclusion that reality must be described solely in terms of field-based formulations.
[1][2] However, it is possible to construct localization observables in terms of positive-operator valued measures that are compatible with the restrictions imposed by the Hegerfeldt theorem.
[3] Specifically, Hegerfeldt's theorem refers to a free particle whose time evolution is determined by a positive Hamiltonian.
If the particle is initially confined in a bounded spatial region, then the spatial region where the probability to find the particle does not vanish, expands superluminarly, thus violating Einstein causality by exceeding the speed of light.