Measurement of Nonlocal Variables without Breaking Causality

TL;DR

This paper explores the conditions under which nonlocal variables can be measured without violating relativistic causality, identifying specific variables that can be measured causally and the information erasure involved.

Contribution

It demonstrates that some nonlocal variables are measurable without causality violation, while others are not, and clarifies the role of local information erasure in causal measurements.

Findings

Certain nonlocal variables can be measured without breaking causality

Measuring entangled states requires erasing local information

Measurability constraints depend on the type of nonlocal variable

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.