A generic qubit unitary operator affected by quantum noise is duplicated and inserted in a coherently superposed channel, superposing two paths offered to a probe qubit across the noisy unitary, and driven by a control qubit. A characterization is performed of the transformation realized by the superposed channel on the joint state of the probe-control qubit pair. The superposed channel is then specifically analyzed for the fundamental metrological task of phase estimation on the noisy unitary, with the performance assessed by the Fisher information, classical or quantum. A comparison is made with conventional estimation techniques and also with a quantum switched channel with indefinite causal order recently investigated for a similar task of phase estimation. In the analysis here, a first important observation is that the control qubit of the superposed channel, although it never directly interacts with the unitary being estimated, can nevertheless be measured alone for effective estimation, while discarding the probe qubit that interacts with the unitary. This property is also present with the switched channel but is inaccessible with conventional techniques. The optimal measurement of the control qubit here is characterized in general conditions. A second important observation is that the noise plays an essential role in coupling the control qubit to the unitary, and that the control qubit remains operative for phase estimation at very strong noise, even with a fully depolarizing noise, whereas conventional estimation and the switched channel become inoperative in these conditions. The results extend the analysis of the capabilities of coherently controlled channels which represent novel devices exploitable for quantum signal and information processing.

中文翻译：

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相干叠加噪声信道上的量子参数估计

受量子噪声影响的通用量子位酉算子被复制并插入到相干叠加通道中，将提供给探针量子位的两条路径叠加在噪声酉域上，并由控制量子位驱动。表征由叠加通道在探针-控制量子位对的联合状态上实现的变换。然后针对噪声幺正相位估计的基本计量任务专门分析叠加信道，性能由经典或量子的 Fisher 信息评估。与传统的估计技术以及最近为类似的相位估计任务研究的具有不确定因果顺序的量子交换信道进行了比较。在这里的分析中，第一个重要的观察结果是叠加通道的控制量子位，虽然它从不直接与被估计的幺正相互作用，但可以单独测量以进行有效估计，同时丢弃与幺正相互作用的探测量子位。这种特性也存在于交换信道中，但传统技术无法达到。这里控制量子位的最佳测量在一般条件下表征。第二个重要的观察结果是噪声在将控制量子位耦合到幺正方面起着至关重要的作用，并且控制量子位在非常强的噪声下仍可用于相位估计，即使是完全去极化噪声，而传统估计和切换通道在这些条件下变得不起作用。