Necessary and sufficient state condition for two-qubit steering using two measurement settings per party and monogamy of steering

TL;DR

This paper derives a necessary and sufficient condition for two-qubit steering with two measurement settings per party, and establishes a tight monogamy relation, advancing the understanding of quantum steering constraints.

Contribution

It provides a new criterion for two-qubit steerability and quantifies the maximum violation, offering insights into the monogamy of quantum steering.

Findings

Derived a criterion for steerability violation

Calculated the maximum quantum violation of the inequality

Established a tight monogamy relation for two-qubit steering

Abstract

We consider the Cavalcanti-Foster-Fuwa-Wiseman inequality~\cite{achsh} which is a necessary and sufficient steerability condition for two-qubit states with two measurement settings on each side. We derive the criterion which an arbitrary two-qubit state must satisfy in order to violate this inequality, and obtain its maximum attainable violation in quantum mechanics. The derived condition on the state parameters enables us to establish a tight monogamy relation for two-qubit steering.