Closed-form criteria for two-qubit steerability and Bell nonlocality

Establish general closed-form criteria that decide whether an arbitrary two-qubit quantum state is steerable or Bell nonlocal, thereby replacing the currently unavailable general analytic tests for these operational abilities.

Background

The paper distinguishes entanglement and teleportation usefulness, for which closed-form criteria are available, from steerability and Bell nonlocality, whose membership tests generally require optimization over measurements or hidden-state/local-variable models. The absence of a general closed-form criterion prevents direct analytic determination of operational thresholds for arbitrary two-qubit noise states.

This unresolved issue motivates the paper’s phase-monotonicity results, which apply to convex, local-unitary-closed ability-absence sets without requiring a closed-form criterion. The paper therefore does not solve the broader problem of deriving such criteria.