Steerability of Rank-2 Two-Qubit Entangled States

Abstract:Quantum nonlocality is an essential resource in quantum information and is commonly classified into three distinct forms: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Gisin's theorem shows that pure-state entanglement implies Bell nonlocality, and it motivates the question of how entanglement and EPR steering are related beyond pure states. Here we prove that every entangled rank-2 two-qubit state is EPR steerable, with rank-1 states included as a special case. The proof combines a local-unitary parametrization of rank-2 two-qubit states, a necessary and sufficient separability condition, and a state-dependent nonlinear steering inequality. This gives an analytical characterization of EPR steerability for rank-2 two-qubit entangled states. Thus, rank-2 two-qubit entangled states provide certifiable EPR-steering resources in quantum information.

Maintext 7 pages + SM 83 pages, 0 figure. Accepted by NPJ Quantum Information

arXiv:2512.22030 [quant-ph]

(or arXiv:2512.22030v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2512.22030 Focus to learn more arXiv-issued DOI via DataCite

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