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Physics Letters A

Tripartite entanglement, coherence, and steering in a two-dimensional electron gas

Chaimae Banouni, M. Mansour, Reem Altuijri, Abdel‐Haleem Abdel‐Aty

Published May 22, 2026• 0 citations
Publisher
DOI
10.1016/j.physleta.2026.131814

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We investigate the relation between tripartite entanglement of the three-qubit system and the maximum steering inequality violation of the reduced two-qubit states. Firstly, it is found that a single parameter family of entangled three-qubit pure states have the maximum steering inequality violation among all of the three-qubit pure states for a fixed amount of tripartite entanglement. The tripartite entanglement is quantified by the genuinely multipartite concurrence, generalized geometric measure, and tangle. Subsequently, the complementary relation between tripartite entanglement and the maximum steering inequality violation for an arbitrary three-qubit pure state can be established. Particularly, the result also holds for three-qubit mixed states if the entanglement measure is tangle. The complementary relations indicate that the maximum steering inequality violation of the reduced two-qubit system is at the expense of tripartite entanglement.
In the present work we study tripartite quantum steering of quantum correlations arising from two local dichotomic measurements on each side in the two types of partially device-independent scenarios: the one-sided device-independent scenario where one of the parties performs untrusted measurements while the other two parties perform trusted measurements and the two-sided device-independent scenario where one of the parties performs trusted measurements while the other two parties perform untrusted measurements. We demonstrate that tripartite steering in the two-sided device-independent scenario is weaker than tripartite steering in the one-sided device-independent scenario by using two families of quantum correlations. That is, these two families of quantum correlations in the two-sided device-independent framework detect tripartite entanglement through tripartite steering for a larger region than that in the one-sided device-independent framework. It is shown that tripartite steering in the two-sided device-independent scenario implies the presence of genuine tripartite entanglement of $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ quantum system, even if the correlation does not exhibit genuine nonlocality or genuine steering.
We investigate the generation of genuine tripartite entanglement in a triangular spin-qubit system due to spatially correlated noise. In particular, we demonstrate how the formation of a highly entangled dark state, a W state, enables robust, long-lived tripartite entanglement. Surprisingly, we find that environmentally induced coherent coupling does not play a crucial role in sustaining this entanglement. This contrasts sharply with the two-qubit case, where the induced coupling significantly influences the entanglement dynamics. Furthermore, we explore two promising approaches to enhance the tripartite entanglement by steering the system toward the dark state: postselection and coherent driving. Our findings offer a robust method for generating high-fidelity tripartite entangled states with potential applications in quantum computation.