Sufficient criterion for guaranteeing that a two-qubit state is unsteerable

TL;DR

This paper introduces a simple criterion for two-qubit states that guarantees unsteerability and Bell locality, revealing new classes of unsteerable entangled states and conditions for measurement compatibility.

Contribution

It presents a novel, easily applicable criterion for unsteerability in two-qubit states, expanding understanding of quantum correlations and measurement compatibility.

Findings

Identifies new classes of unsteerable entangled states

Provides conditions for one-way steerability

Establishes a criterion for joint measurability of qubit measurements

Abstract

Quantum steering can be detected via the violation of steering inequalities, which provide sufficient conditions for the steerability of quantum states. Here we discuss the converse problem, namely ensuring that a state is unsteerable, and hence Bell local. We present a simple criterion, applicable to any two-qubit state, which guarantees that the state admits a local hidden state model for arbitrary projective measurements. We find new classes of unsteerable entangled states, which can thus not violate any steering or Bell inequality. In turn, this leads to sufficient conditions for a state to be only one-way steerable, and provides the simplest possible example of one-way steering. Finally, by exploiting the connection between steering and measurement incompatibility, we give a sufficient criterion for a continuous set of qubit measurements to be jointly measurable.