Quantum steering under constrained free-will

TL;DR

This paper investigates quantum steering when measurement choices are biased by an adversary, introducing measurement-dependent steering inequalities and analyzing their implications for certifying quantum randomness.

Contribution

It introduces the measurement-dependent steering framework, develops inequalities for detecting MD-steerable correlations, and explores bounds on measurement dependence for observed correlations.

Findings

Derived inequalities for MD-steerability detection

Established bounds on measurement dependence for correlations

Discussed implications for quantum randomness certification

Abstract

Quantum steering is a kind of bipartite quantum correlations where one party's measurement remotely alters the state of another party. In an adversarial scenario, there could be a hidden variable introducing a bias in the choice of measurement settings of the parties. However, observers without access to the hidden variable are unaware of this bias. The main focus of this work is to analyze quantum steering without assuming that the parties freely choose their measurement settings. For this, we introduce the measurement-dependent (MD-)steering scenario where the measurement settings chosen by the parties are biased by an adversary. In such a scenario, we present a class of inequalities to test for MD-steerable correlations. Further, we discuss the implications of violating such inequalities in certifying randomness from quantum extremal behaviors. We also assume that an adversary might prepare an assemblage as a mixture of MD-steerable and MD-unsteerable assemblages and provide a bound on the measurement dependence for the observed correlation to remain MD-steerable.