Practical and Reliable Error Bars in Quantum Tomography
Practical and Reliable Error Bars in Quantum Tomography
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DOI：
10.1103/physrevlett.117.010404
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发表时间：
2016-07-01
影响因子：
8.6
通讯作者：
Renner, Renato
中科院分区：
文献类型：
--
作者：
Faist, Philippe;Renner, Renato
量子器件的精确表征通常是通过量子层析成像来实现的。然而，目前在实验中广泛使用的大多数方法，如最大似然估计，都缺乏合理的误差分析。最近有希望的基于置信域的方法很难在实践中应用，或者产生不必要的大误差条。在这里，我们提出了一种实用而稳健的获得误差条的方法。为此，我们引入了层析成像过程的输出的一种新的表示，量子误差条。这种表示是(I)简明的，以很少的参数给出，(Ii)直观，提供了误差“扩散”的合理概念，以及(Iii)有用，包含了构造置信域所需的信息。由我们的方法产生的陈述是用品质因数来表示的，例如对参考状态的保真度。我们提出了一种计算这种表示的算法，并提供了现成的软件。我们的方法被应用于两个处于纠缠态的超导量子比特的实际实验数据，证明了我们方法的适用性。
Precise characterization of quantum devices is usually achieved with quantum tomography. However, most methods which are currently widely used in experiments, such as maximum likelihood estimation, lack a well-justified error analysis. Promising recent methods based on confidence regions are difficult to apply in practice or yield error bars which are unnecessarily large. Here, we propose a practical yet robust method for obtaining error bars. We do so by introducing a novel representation of the output of the tomography procedure, the quantum error bars. This representation is (i) concise, being given in terms of few parameters, (ii) intuitive, providing a fair idea of the "spread" of the error, and (iii) useful, containing the necessary information for constructing confidence regions. The statements resulting from our method are formulated in terms of a figure of merit, such as the fidelity to a reference state. We present an algorithm for computing this representation and provide ready-to-use software. Our procedure is applied to actual experimental data obtained from two superconducting qubits in an entangled state, demonstrating the applicability of our method.