Protection of quantum steering ellipsoids in non-Markovian environments

Abstract: The quantum steering ellipsoid (QSE) provides a geometric representation, within the Bloch picture, of all possible states to which one qubit can be steered through measurements performed on another correlated qubit. However, in most realistic settings, quantum systems are inevitably coupled to their surrounding environment, resulting in decoherence and the consequent degradation of the QSE. Here, by investigating how local dissipative environments coupled separately to each qubit affect the steering properties geometrized by the QSE within an exact non-Markovian framework, we find that the geometry of each party's QSE is closely tied to whether a bound state forms in the energy spectrum of the total qubit-environment system. We systematically examine the characteristics of QSEs under three distinct scenarios: two-sided bound states, one-sided bound states, and no bound state, revealing a diverse range of steering types. Our work establishes quantum reservoir engineering as a tunable strategy for protecting and controlling quantum steering in open systems, offering a practical pathway toward robust steering-based quantum technologies.