Optimizing Quantum Entanglement Preservation in a Qubit Qubit System with Dzyaloshinskii Moriya Interaction under Noisy Magnetic Fields via Feedback Control

Abstract

Quantum entanglement is a key resource for quantum information processing and sensing, but it is severely degraded by environmental noise. We extend the previous study by Moosavi Khansari and Kazemi Hasanvand [27] of entanglement dynamics in a qubit qubit system with Dzyaloshinskii Moriya (DM) interaction and static magnetic fields to the realistic case of time varying, stochastic magnetic fields. We derive a stochastic Lindblad master equation and simulate quantum trajectories to quantify the negativity under colored noise. We then design a proportional integral feedback protocol that dynamically adjusts the DM interaction strength D_z (t) to maintain negativity near a target value. The feedback stabilized state is used as a probe for quantum metrology: we compute the quantum Fisher information (QFI) for estimating an unknown static field B_0. Our simulations show that feedback increases the time averaged negativity from 0.21 to 0.42 for α=1 at noise amplitude σ=0.5, leading to a factor 2.5 improvement in sensitivity over the classical shot noise limit. This work provides a practical route to protect entanglement in noisy environments and enhances quantum sensing performance.