Quantum tomography is a class of characterization methods frequently used in current experiments, but its standard protocols suffer from unreliability originated from preknowledge assumptions. Self-consistent quantum tomography is an approach to avoid the problem, which treats every quantum operation in a characterization experiment as unknown objects to be characterized. As compensation for the beneficence, it leads to a problem that its characterization results cannot be determined uniquely only from experimental data due to the existence of experimentally undetectable gauge degrees of freedom, and we need to introduce a criterion to fix the gauge. Here, we propose to use a regularization technique to fix the gauge. First, we derive a sufficient condition on a characterization experiment to obtain all information of objects to be characterized except for the gauge. Second, we propose a self-consistent data-processing method with regularization and physicality constraints. A careless use of regularization can lead to non-negligible bias on the characterization result. As a solution for the concern, we propose a concrete way to tune the strength of the regularization, and mathematically prove that the method provides characterization results that converge to the gauge-equivalence class of the quantum operations of interest at the limit of data going to infinity. The asymptotic convergence guarantees the reliability of the method. We also derive the asymptotic convergence rate, which would be optimal. These theoretical results hold for any finite-dimensional quantum systems. Finally, as its first numerical implementation, we show numerical results on one-qubit system, which confirm the theoretical results and prove that the method proposed is practical.

中文翻译：

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具有正则化的自洽量子断层扫描

量子断层扫描是当前实验中经常使用的一类表征方法，但其标准协议存在源于预知假设的不可靠性。自洽量子断层扫描是一种避免该问题的方法，它将表征实验中的每个量子操作都视为待表征的未知对象。作为对善意的补偿，由于存在实验无法检测的规范自由度，导致其表征结果不能唯一确定仅由实验数据确定的问题，我们需要引入一个标准来固定规范。在这里，我们建议使用正则化技术来固定仪表。第一的，我们在表征实验上推导出一个充分条件，以获得除规范外的所有待表征对象的信息。其次，我们提出了一种具有正则化和物理约束的自洽数据处理方法。对正则化的粗心使用可能会导致对表征结果的不可忽视的偏差。作为该问题的解决方案，我们提出了一种具体的方法来调整正则化的强度，并在数学上证明该方法提供的表征结果收敛到感兴趣的量子操作的规范等价类在数据的限制下无限。渐近收敛保证了方法的可靠性。我们还推导出渐近收敛率，这将是最优的。这些理论结果适用于任何有限维量子系统。最后，作为它的第一个数值实现，我们在一个量子位系统上展示了数值结果，这证实了理论结果并证明了所提出的方法是可行的。