Dynamics of Einstein-Podolsky-Rosen Steering in Quantum Spin Environment

We explore the dynamics of Einstein-Podolsky-Rosen steering (EPR), measured by steering robustness, for two spin-qubits coupled to a general XY spin chain environment. The evolution process is numerically investigated in the vicinity of critical point for the spin environment. The results show an obvious suppression of steering robustness when the environment undergoes a quantum phase transition. The scaling behavior for the dynamics of EPR steering is also revealed and analyzed around the critical point. Furthermore, we find that steering robustness power (i.e. the average value of steering robustness within a certain time) can indicate the quantum criticality of the environment directly.