  We show that the nondemolition measurement of a spacelike Wilson loop
operator W(C) is impossible in a relativistic non-Abelian gauge theory. In
particular, if two spacelike-separated magnetic flux tubes both link with the
loop C, then a nondemolition measurement of W(C) would cause electric charge to
be transferred from one flux tube to the other, a violation of relativistic
causality. A destructive measurement of W(C) is possible in a non-Abelian gauge
theory with suitable matter content. In an Abelian gauge theory, many
cooperating parties distributed along the loop C can perform a nondemolition
measurement of the Wilson loop operator if they are equipped with a shared
entangled ancilla that has been prepared in advance. We also note that Abelian
electric charge (but not non-Abelian charge) can be transported superluminally,
without any accompanying transmission of information.
