Measurability of Wilson loop operators

TL;DR

This paper demonstrates the fundamental limitations on measuring Wilson loop operators in relativistic gauge theories, highlighting differences between Abelian and non-Abelian cases and implications for causality.

Contribution

It establishes the impossibility of nondemolition measurements of Wilson loops in non-Abelian theories and explores measurement strategies in Abelian theories with shared entanglement.

Findings

Nondemolition measurement of Wilson loops is impossible in non-Abelian gauge theories.

Destructive measurements of Wilson loops are feasible with suitable matter content.

Abelian electric charge can be transported superluminally without transmitting information.

Abstract

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.