Quantum temporal steering in a noise channel with topological characterization

Abstract

We explore quantum temporal steering, measured by temporal steering robustness ${\mathcal {R}}_\mathrm{TS}$, in a quantum channel $\varLambda$ 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 $\lambda$, we find that ${\mathcal {R}}_\mathrm{TS}$ is remarkably depressed. Moreover, ${\mathcal {R}}_\mathrm{TS}$ exhibits a finite-size scaling behavior in the vicinity of TQPT points. Meanwhile, by calculating the temporal steering robustness power $P_{{\mathcal {R}}}$, we can get the environment channel’s phase diagram which is exactly similar with the one obtained by topological quantity, i.e., winding number ${\mathcal {N}}$. Additionally, we also analyze the behaviors of ${\mathcal {R}}_\mathrm{TS}$ when the environment channel is driven by other parameters (i.e., anisotropy of nearest-neighbor interaction $\gamma$, three-site interactions $\alpha$ and anisotropy of three-site interactions $\delta$). The results show that ${\mathcal {R}}_\mathrm{TS}$ approaches to zero quickly in a short time t at all the TQPT points and $P_{{\mathcal {R}}}$ can also highlight these points exactly for all driving parameters.

Graphic abstract