In this paper, we propose a feed-forward control approach to protect arbitrary two-qubit pure and mixed initial states using the weak measurement. A feed-forward operation and measurements are used before the noise channel, and afterward, a reversed operation and measurements are applied to recover the state back to its initial state. In the case of two-qubit pure states, we use the unraveling trick to describe the state of the system in each step of the control procedure. For two-qubit mixed states, a completely positive trace-preserving map is implemented. Finally, the fidelity and success probability are used to evaluate the effect of protection. The complete recovery conditions for the measurement strengths are derived, under which we achieve the optimal fidelity and the success probability of recovering the initial pure and mixed states.

中文翻译：

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基于弱测量的幅度阻尼恢复两比特状态

在本文中，我们提出了一种前馈控制方法，以使用弱测量来保护任意的两比特纯净和混合初始状态。在噪声通道之前先进行前馈操作和测量，然后再进行反向操作和测量，以将状态恢复到其初始状态。在两个量子位纯状态的情况下，我们使用分解技巧来描述控制过程每一步中的系统状态。对于两个量子位的混合状态，将实现一个完全正的迹线保留映射。最后，将保真度和成功概率用于评估保护效果。导出了测量强度的完全恢复条件，在此条件下，我们获得了最佳保真度以及恢复初始纯态和混合态的成功概率。