Lack of measurement independence can simulate quantum correlation even when signaling cannot

TL;DR

This paper demonstrates that in semi-quantum scenarios, quantum correlations can be simulated by reducing measurement independence without signaling, highlighting a fundamental difference from traditional Bell scenarios.

Contribution

It reveals that measurement independence reduction can simulate quantum correlations in semi-quantum scenarios, unlike in Bell scenarios, and distinguishes between signaling and measurement dependence.

Findings

Entangled states produce correlations explainable only with reduced measurement independence in semi-quantum scenarios.

Distinction between signaling and measurement dependence is absent in steering game scenarios.

Semi-quantum scenario exposes a qualitative difference not seen in Bell scenarios.

Abstract

In Bell scenario, any nonlocal correlation, shared between two spatially separated parties, can be modeled deterministically either by allowing communications between the two parties or by restricting their free will in choosing the measurement settings. Recently, Bell scenario has been generalized into `semi-quantum' scenario where external quantum inputs are provided to the parties. We show that in `semi-quantum' scenario, entangled states produce correlations whose deterministic explanation is possible only if measurement independence is reduced. Thus in simulating quantum correlation `semi-quantum' scenario reveals a qualitative distinction between signaling and measurement dependence which is absent in Bell scenario. We further show that such distinction is not observed in `steering game' scenario, a special case of `semi-quantum' scenario.