Quantum Algorithm for Petz Recovery Channels and Pretty Good Measurements
Quantum Algorithm for Petz Recovery Channels and Pretty Good Measurements
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DOI：
10.1103/physrevlett.128.220502
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发表时间：
2022-06-01
影响因子：
8.6
通讯作者：
Wilde, Mark M.
中科院分区：
文献类型：
--
作者：
Gilyen, Andras;Lloyd, Seth;Wilde, Mark M.
PETZ恢复通道在量子信息科学中起着重要的作用，作为近似逆转量子通道效果的操作。非常好的测量是PETZ恢复渠道的特殊情况，它允许近乎最佳的状态歧视。这些自负的理论工具实现实验性实现的障碍是缺乏实施它们的系统和高效方法。这封信旨在纠正这种缺乏：使用最近开发的量子奇异值转换和忘记振幅放大工具，我们提供了一种量子算法来实现PETZ恢复通道，以执行人们希望逆转的通道。此外，我们证明，从某种意义上说，我们的量子算法对渠道实现的使用不能超过二次因素的改进。当给出一个试图区分的州的多个副本时，我们的量子算法还提供了执行相当不错的测量的过程。
The Petz recovery channel plays an important role in quantum information science as an operation that approximately reverses the effect of a quantum channel. The pretty good measurement is a special case of the Petz recovery channel, and it allows for near-optimal state discrimination. A hurdle to the experimental realization of these vaunted theoretical tools is the lack of a systematic and efficient method to implement them. This Letter sets out to rectify this lack: Using the recently developed tools of quantum singular value transformation and oblivious amplitude amplification, we provide a quantum algorithm to implement the Petz recovery channel when given the ability to perform the channel that one wishes to reverse. Moreover, we prove that, in some sense, our quantum algorithm???s usage of the channel implementation cannot be improved by more than a quadratic factor. Our quantum algorithm also provides a procedure to perform pretty good measurements when given multiple copies of the states that one is trying to distinguish.