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Symmetric quantum correlations and their properties have been investigated extensively in spin chain model under decoherence. However, the asymmetric ones, e.g., Einstein–Podolsky–Rosen steering, have been attracted smaller amount of attention in this issue. In this work, we study the dynamics of Einstein–Podolsky–Rosen steering, measured by steering robustness R, for a two-qubit Heisenberg XYZ chain with inhomogeneous magnetic field by taking account of decoherence effect. The influences of magnetic field and anisotropic parameter on steering robustness are investigated for different initial states. It is found that the phenomenon of steering sudden death as well as sudden birth appears during the evolution process for particular initial states. Furthermore, the asymmetric property of Einstein–Podolsky–Rosen steering is focused and analyzed in detail. It is shown that the asymmetric steering is directly linked to the initial state as well as the external non-uniform magnetic field. Meanwhile, we find that there always exists asymmetric steering even the magnetic field is homogeneous for both the initial two-qubit pure state | 10 ⟩ and asymmetry mixed ones. [ABSTRACT FROM AUTHOR]

We explore quantum temporal steering, measured by temporal steering robustness R TS , in a quantum channel Λ described by a qubit coupling to an extended anisotropic XY spin chain associated with non-trivial topological characterization. When the environment channel undergoes a topological quantum phase transition (TQPT), driven by magnetic field λ , we find that R TS is remarkably depressed. Moreover, R TS exhibits a finite-size scaling behavior in the vicinity of TQPT points. Meanwhile, by calculating the temporal steering robustness power P R , we can get the environment channel's phase diagram which is exactly similar with the one obtained by topological quantity, i.e., winding number N . Additionally, we also analyze the behaviors of R TS when the environment channel is driven by other parameters (i.e., anisotropy of nearest-neighbor interaction γ , three-site interactions α and anisotropy of three-site interactions δ ). The results show that R TS approaches to zero quickly in a short time t at all the TQPT points and P R can also highlight these points exactly for all driving parameters. [ABSTRACT FROM AUTHOR]