Ascertaining the influences of auxiliary qubits on the Einstein-Podolsky-Rosen steering and its directions

Einstein-Podolsky-Rosen (EPR) steering is one of nontrivial quantum nonlocalities and characteristics in the non-classical world. The directivity (or asymmetry) is a fascinating trait of the EPR steering, and it is different from other quantum nonlocalities. Here, considering the strategy in which two atoms compose a two-qubit X state, and the two atoms are owned by Alice and Bob, respectively. The atom of Alice suffers from a reservoir, and the atom of Bob couples with a bit flip channel. The influences of auxiliary qubits on the EPR steering and its directions are revealed by means of entropy uncertainty relation. The results indicate that the EPR steering declines with growing time t when adding less auxiliary qubits. The EPR steering behaves as damped oscillation when introducing more auxiliary qubits in the strong coupling regime. In the weak coupling regime, the EPR steering monotonously decreases as t increases when coupling auxiliary qubits. The increases of auxiliary qubits are responsible for the fact that the steerability from Alice to Bob (or from Bob to Alice) can be more effectively revealed. Notably, the introductions of more auxiliary qubits can change the situation that the steerability from Alice to Bob is certain into the situation that the steerability from Bob to Alice is certain.