Quantum temporal steering in a dephasing channel with quantum criticality

We investigate the quantum temporal steering (TS), i.e., a temporal analogue of Einstein-Podolsky-Rosen steering, in a dephasing channel which is modeled by a central spin half surrounded by a spin-1/2 \textit{XY} chain where quantum phase transition happens. The TS parameter $S_{\text{TS}}$ and the TS weight $W_{\text{TS}}$ are employed to characterize the TS dynamics. We analytically obtain the dependence of $S_{\text{TS}}$ on the decoherence factor. The numerical results show an obvious suppression of $S_{\text{TS}}$ and $W_{\text{TS}}$ when the \textit{XY} chain approaches to the critical point. In view of the significance of quantum channel, we develop a new concept, \textit{TS weight power}, in order to quantify the capacity of the quantum channel in dominating TS behavior. This new quantity enables us to indicate the quantum criticality of the environment by the quantum correlation of TS in the coupled system.