Background Dependence of Local States

Abstract

We consider states prepared by a series of actions performed in a finite space‐time region in the presence of a background state described by a density matrix. It is shown that there will always be some observable whose expectation value in such a state will depend to some extent on the background. There will, however, be a certain set of observables whose expectation values will be independent of the background. We obtain a characterization of such sets of observables.