Quantum temporal steering in a dephasing channel with quantum criticality

TL;DR

This paper studies quantum temporal steering in a dephasing channel influenced by a quantum critical environment, revealing how criticality suppresses quantum correlations and introducing a new measure to quantify channel capacity.

Contribution

It introduces the concept of TS weight power to quantify the environment's quantum criticality through temporal steering behavior.

Findings

TS parameters decrease near the critical point

Quantum criticality affects quantum channel capacity

Analytical and numerical methods confirm environment influence

Abstract

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.