Operationally independent events can influence each other in quantum theory

TL;DR

This paper demonstrates that in quantum theory, two systems can influence each other without observable effects, challenging classical notions of independence, with implications for quantum certification.

Contribution

It introduces a framework showing quantum systems can influence each other without observable effects, using a linear witness and Bell inequality in quantum networks.

Findings

Quantum systems can influence each other without observable effects.

Maximal violation of classical independence aids in device-independent quantum certification.

A new linear witness based on CHSH inequality is constructed.

Abstract

In any known description of nature, two physical systems are considered independent of each other if any action on one of the systems does not change the other system. From our classical intuitions about the world, we further conclude that these two systems are not affecting each other in any possible way, and thus these two systems are causally disconnected or they do not influence each other. Building on this idea, we show that in quantum theory such a notion of classical independence is not satisfied, that is, two quantum systems can still influence each other even if any operation on one of the systems does not create an observable effect on the other. For our purpose, we consider the framework of quantum networks and construct a linear witness utilizing the Clauser-Horne-Shimony-Holt inequality. We also discuss one of the interesting applications resulting from the maximal violation of classical independence towards device-independent certification of quantum states and measurements.