Measurement of Nonlocal Variables without Breaking Causality

Abstract

We report results of an investigation of relativistic causality constraints on the measurability of nonlocal variables. We show that measurability of certain nondegenerate variables with entangled eigenstates contradicts the principle of causality, but that there are other, certainly nonlocal, variables which can be measured without breaking causality. We show that any causal measurement of nonlocal variables must erase certain local information. For example, for a system of two spin-1/2 particles, even if we take the weakest possible definition of verification measurement, verification of an entangled state must erase all local information.