Self-consistent quantum tomography with regularization
Self-consistent quantum tomography with regularization
复制标题
具有正则化的自洽量子层析成像
DOI：
10.1103/physreva.103.062615
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发表时间：
2021
影响因子：
2.9
通讯作者：
Tanaka Fuyuhiko
中科院分区：
文献类型：
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作者：
Sugiyama Takanori;Imori Shinpei;Tanaka Fuyuhiko
量子层析成像是当前实验中常用的一类表征方法，但其标准协议存在先验假设的不可靠性。自洽量子层析成像是一种避免这一问题的方法，它将表征实验中的每一个量子操作都视为待表征的未知对象。作为补偿，由于存在着实验上不可测的规范自由度，导致了仅从实验数据不能唯一确定其表征结果的问题，需要引入一个规范固定准则。在这里，我们建议使用正则化技术来固定规范。首先，我们得到了一个充分条件的表征实验，以获得所有的信息，除了规范的对象进行表征。其次，我们提出了一个具有正则化和物理约束的自洽数据处理方法。不小心使用正则化可能会导致表征结果上的不可忽略的偏差。作为一个解决方案的关注，我们提出了一个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规范等价类的量子操作的数据的极限无穷大。渐近收敛性保证了方法的可靠性。我们还得到了渐近收敛速度，这将是最佳的。这些理论结果适用于任何有限维量子系统。最后，作为该方法的第一个数值实现，我们给出了单量子比特系统的数值结果，验证了理论结果，证明了该方法的实用性。
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.