Practical quantum metrology is generally hindered by environment noise which can demolish the advantage of breaching the shot-noise limit provided by quantum mechanics. Recently, quantum error-correction (QEC) codes have been developed for restoring the quantum advantage against Markovian noise for quantum metrology. This has been done by assuming either the existence of noiseless ancilla or specific noise types such as the spatially correlated noise and the so-called commuting noise. We consider the situation where all probing systems for metrology are infested by general uncorrelated Markovian noise; namely, there is neither noiseless ancilla nor spatial correlation of the noise. Under such circumstances, we have discussed the error-correction conditions in parallel metrology scheme where more than three probes are employed. We have shown the superiority of parallel schemes over sequential schemes in fighting Markovian noise by ancilla-free QEC with an explicit example. If we employ qubits for parameter sensing, it can be shown that one can restore Heisenberg limit (HL) via full and fast control without any ancilla, as long as the signal Hamiltonian of the probe system has nonvanishing component perpendicular to the noise. This is exactly the same requirement for restoring HL with the assistance of noiseless ancilla.

中文翻译：

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在没有马尔可夫噪声的情况下使用量子误差校正来实现海森堡极限

实际的量子计量通常受到环境噪声的阻碍，环境噪声会破坏突破量子力学提供的散粒噪声限制的优势。近来，已经开发了量子纠错（QEC）码以恢复针对马尔可夫噪声的量子优势以用于量子计量。这是通过假设存在无噪声辅助音或特定噪声类型（例如空间相关噪声和所谓的通勤噪声）来完成的。我们考虑这样一种情况，所有的计量学探测系统都受到一般不相关的马尔可夫噪声的干扰；即，既没有无噪音的辅助，也没有噪音的空间相关性。在这种情况下，我们讨论了采用三个以上探头的并行计量方案中的纠错条件。我们通过一个无实例的QEC展示了在对抗Markovian噪声方面，并行方案优于顺序方案的优越性。如果我们使用量子位进行参数感测，则可以证明，只要探针系统的信号哈密顿量具有与噪声垂直的不变分量，就可以通过完全而快速的控制来恢复海森堡极限（HL），而不会出现任何辅助现象。这与在无噪音辅助装置的帮助下恢复HL的要求完全相同。只要探测系统的信号哈密顿量具有垂直于噪声的无消失分量即可。这与在无噪音辅助装置的帮助下恢复HL的要求完全相同。只要探测系统的信号哈密顿量具有垂直于噪声的无消失分量即可。这与在无噪音辅助装置的帮助下恢复HL的要求完全相同。