# Time Evolution of Quantum Entanglement of an EPR Pair in a Localized Environment

## TL;DR

This paper studies how quantum entanglement of an EPR pair evolves over time in disordered environments, revealing different behaviors in Anderson localized and many-body localized phases, with implications for quantum information preservation.

## Contribution

It provides a theoretical analysis of entanglement dynamics in AL and MBL phases, highlighting their distinct effects on quantum resource stability and phase identification.

## Key findings

- Entanglement approaches a plateau in AL phase.
- Power-law decay of entanglement in MBL phase.
- Potential use of entanglement dynamics to distinguish phases.

## Abstract

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.