Extreme volume monogamy via bound-state engineering

Abstract: Quantum steering ellipsoid (QSE) provides a faithful representation of a two-qubit state. When extended to tripartite systems, the steerability from a trusted party to different receivers is subject to volume monogamy relations, which only constrain the total steerability but cannot individually eliminate the steerability of an untrusted third party, leaving a potential channel for information leakage via steering. Here, we show that this residual steerability can be completely suppressed by selectively engineering bound states in local qubit-environment subsystems, without compromising the steerability between trusted parties. Specifically, when bound states are formed in the subsystems formed by the trusted parties and their environments but absent in the untrusted one, the untrusted party's QSE volume decays to zero, while the trusted party's QSE volume remains finite. Our results establish selective bound-state engineering as a mechanism for extreme volume monogamy, with potential applications in secure quantum communication with an untrusted third party.