Uncertainty-Complementarity Balance as a General Constraint on Non-locality

TL;DR

This paper introduces a theory-independent uncertainty-complementarity balance relation linking non-locality, complementarity, and uncertainty, deriving bounds like Tsirelson's and analyzing non-local theories including PR boxes.

Contribution

It formulates a universal balance relation connecting uncertainty and complementarity, deriving non-local bounds and applying it to various theoretical scenarios.

Findings

Quantum theory respects the balance relation.

Tsirelson's bound is derived from the balance relation.

Non-local bounds are expressed as functions of balance strength.

Abstract

We propose an uncertainty-complementarity balance relation and build quantitative connections among non-locality, complementarity, and uncertainty. Our balance relation, which is formulated in a theory-independent manner, states that for two measurements performed sequentially, the complementarity demonstrated in the first measurement in terms of disturbance is no greater than the uncertainty of the first measurement. Quantum theory respects our balance relation, from which the Tsirelson bound can be derived, up to an inessential assumption. In the simplest Bell scenario, we show that the bound of Clauser-Horne-Shimony-Holt inequality for a general non-local theory can be expressed as a function of the balance strength, a constance for the given theory. As an application, we derive the balance strength as well as the nonlocal bound of Popescu-Rohrlich box. Our results shed light on quantitative connections among three fundamental concepts, i.e., uncertainty, complementarity and non-locality.