Entanglement Protection Using Weak Measurement in Non-Markovian Environment

In this work, a scheme to protect quantum entanglement from a non-Markovian noisy environment is proposed. By applying two quantum weak measurements before and after sending the quantum state into the noisy channel, the quantum state can be “pushed” closer to a decoherence-free state, reducing decoherence during the time evolution. Then, the second weak measurement can partially retrieve the initial quantum state from the state corrupted by the noisy environment. The study involves a non-Markovian dynamic equation to examine the impact of the memory effect on the protection scheme's performance. Various factors affecting the residual entanglement and the success probability are analyzed. The results suggest that two measurement strengths shall be chosen approximately in a linear relation, with the best ratio determined by the memory time of the environment. Additionally, it is demonstrated that the memory effect significantly enhances the protection efficiency. Lastly, the scheme's robustness against systematic errors is evaluated.