  The Einstein-Podolsky-Rosen (EPR) pair of qubits plays a critical role in
many quantum protocol applications such as quantum communication and quantum
teleportation. Due to interaction with the environment, an EPR pair might lose
its entanglement and can no longer serve as useful quantum resources. On the
other hand, it has been suggested that introducing disorder into environment
might help to prevent thermalization and improve the preservation of
entanglement. Here, we theoretically investigate the time evolution of quantum
entanglement of an EPR pair in a random-field XXZ spin chain model in the
Anderson localized (AL) and many-body localized (MBL) phase. We find that the
entanglement between the qubits decreases and approaches to a plateau in the AL
phase, but shows a power-law decrease after some critical time determined by
the interaction strength in the MBL phase. Our findings, on one hand, shed
lights on applying AL/MBL to improve quantum information storage; on the other
hand, can be used as a practical indicator to distinguish the AL and MBL phase.
