Abstract The dynamics behaviors of genuine multipartite Einstein–Podolsky–Rosen steering (GMS) and genuine multipartite nonlocality (GMN) are investigated herein, and how the lost GMS and GMN under a mixed decoherence system can be recovered is explored. Explicitly, the decoherence system can be modeled by that a tripartite Werner‐type state suffers from the non‐Markovian regimes and one subsystem of the tripartite is under a non‐inertial frame. The conditions for steerable and nonlocal states can be obtained with respect to the tripartite Werner‐type state established initially. GMS and GMN are very fragile and vulnerable under the influence of the collective decoherence. GMS and GMN will vanish with growing intensity of the Unruh effect and the non‐Markovian reservoir. Besides, all achievable GMN's states are steerable, while not every steerable state (GMS's state) can achieve nonlocality. This means that the steering–nonlocality hierarchy is still tenable and GMN's states are a strict subset of the GMS's states in such a scenario. Subsequently, an available methodology to recover the damaged GMS and GMN is proposed. It turns out that the lost GMS and GMN can be effectively restored, and the ability of GMS and GMN to suppress the collective decoherence can be enhanced.
Spin-
21 two-leg ladder models under a magnetic field have a well-known phase diagram. In this paper, we use multipartite nonlocality (a measure of multipartite quantum correlations) to characterize the quantum correlations in the ladder models at zero temperature. Both finite-size and infinite-size ladders are considered. We investigate the global nonlocality ${\mathcal{S}}_{g}=\mathcal{S}(|{\mathrm{\ensuremath{\Psi}}}_{g}\ensuremath{\rangle})$, which describes quantum correlations of the ground states $|{\mathrm{\ensuremath{\Psi}}}_{g}\ensuremath{\rangle}$ of the entire lattices, and the partial nonlocality ${\mathcal{S}}_{p}=\mathcal{S}({\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{n})$, which describes quantum correlations of the reduced states ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{n}$ of some sublattices in the ladders. We find that as the magnetic field $\ensuremath{\lambda}$ increases, the global nonlocality
Sg presents a single-peak curve. Moreover, the logarithmic measure
lnSg changes dramatically at the two critical fields ${\ensuremath{\lambda}}_{{c}_{1}}$ and ${\ensuremath{\lambda}}_{{c}_{2}}$ of the models and thus signals the quantum phase transitions in the models. For the partial nonlocality
Sp, in the regions ${\ensuremath{\lambda}}_{{c}_{1}}<\ensuremath{\lambda}<{\ensuremath{\lambda}}_{{c}_{2}}$, we observe that the ${\mathcal{S}}_{p}(\ensuremath{\lambda})$ curve shows an oscillation. Numerical results reveal that the underling mechanism is the ``major component transitions'' in the reduced states ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{n}$ of the sublattices. More importantly, the oscillation of the partial nonlocality
Sp is modulated by the single-peak curve of the global nonlocality
Sg. The result provides valuable clues about the relation between partial nonlocality and global nonlocality in low-dimensional quantum models.
Quantum nonlocality manifests in multipartite systems through entanglement, Bell's nonlocality, and Einstein-Podolsky-Rosen (EPR) steering. While Peres's positive-partial-transpose criterion provides a simple and powerful test for entanglement, a comparably elegant spectral criterion for detecting EPR steering remains an open challenge. In this work, we systematically explore whether a Peres-type criterion can be established for EPR steering in the two-qubit system. Focusing on rank-2 (including rank-1) states and the two-qubit Werner state, we analyze the eigenvalues of their partially transposed density matrices and construct a significant steering criterion based on symmetric combinations of these eigenvalues. We prove that this criterion serves as a necessary and sufficient condition for steerability for the Werner state, all two-qubit pure states, all two-qubit rank-2 states. Furthermore, we validate the criterion for higher-rank states (rank-3 and rank-4) and show that the results align with known steering inequalities. Our findings suggest a more unified framework for detecting quantum nonlocality via partial transposition and open avenues for further theoretical and numerical investigations into steering detection.