arXiv 1701.017642017-01-06quant-ph

量子层析成像的高效和鲁棒方法

Efficient and Robust Methods for Quantum Tomography

Charles H. Baldwin

备注：: Ph.D. Thesis, 180 pages

摘要：

大规模量子信息平台的发展需要新的方法来验证和确认量子行为。量子层析成像（QT）是通过提供完整信息来诊断量子态、过程和读出设备的标准工具。然而，QT是有限的，因为它不仅是昂贵的实验实现，而且还需要大量的经典的数据后处理。在这篇论文中，我们介绍了新的方法，QT是更有效的实现和鲁棒性的噪声和错误，从而使QT更实用的工具，为当前的量子信息实验。使这些新的、有效的和鲁棒的方法成为可能的关键细节是关于量子系统的先验信息。这种先验信息是由量子信息中的大多数实验的目标所促使的，这些实验需要纯态、幺正过程和秩1 POVM算子。因此，大多数实验都设计成在这个理想状态附近操作。我们表明，在这种情况下，QT可以用更少的资源来完成，并在存在噪声和误差的情况下产生鲁棒的估计。此外，如果状态不完全是纯的，过程不完全是酉的，或者POVM不完全是秩-1，估计也是鲁棒的。只有通过对量子态、过程和POVM的正性约束，才有可能实现这种令人信服的方法。这一要求是量子力学的固有特征，但对QT有很强的影响。由于QT必然是一种实验工具，因此我们讨论了在实验环境中对这些新方法的测试。该物理系统是Poul Reichen教授实验室中的激光冷却铯原子系综。Hector Sosa-Martinez等人进行了实验，以证明不同的QT方案。通过对计算结果的比较，证明了新方法的有效性。

英文摘要：

The development of large-scale platforms for quantum information requires new methods for verification and validation of quantum behavior. Quantum tomography (QT) is the standard tool for diagnosing quantum states, process, and readout devices by providing complete information. However, QT is limited since it is expensive to not only implement experimentally, but also requires heavy classical post-processing of data. In this dissertation, we introduce new methods for QT that are more efficient to implement and robust to noise and errors, thereby making QT a more practical tool for current quantum information experiments. The crucial detail that makes these new, efficient, and robust methods possible is prior information about the quantum system. This prior information is prompted by the goals of most experiments in quantum information, which require pure states, unitary processes, and rank-1 POVM operators. Therefore, most experiments are designed to operate near this ideal regime. We show that when this is the case, QT can be accomplished with significantly fewer resources, and produce a robust estimate in the presence of noise and errors. Moreover, the estimate is also robust if the state is not exactly pure, the process is not exactly unitary, or the POVM is not exactly rank-1. Such compelling methods are only made possible by the positivity constraint on quantum states, processes, and POVMs. This requirement is an inherent feature of quantum mechanics, but has powerful consequences to QT. Since QT is necessarily an experimental tool, we discuss a test of these new methods in an experimental setting. The physical system is an ensemble of laser-cooled cesium atoms in the laboratory of Prof. Poul Jessen. Experiments were conducted by Hector Sosa-Martinez et al. to demonstrate different QT protocols. We compare the results, and conclude that the new methods are effective.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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