Quantum Algorithm for Petz Recovery Channels and Pretty Good Measurements
Author(s)
Gilyén, András; Lloyd, Seth; Marvian, Iman; Quek, Yihui; Wilde, Mark M.
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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.
Date issued
2022-06-01Department
Massachusetts Institute of Technology. Department of Mechanical Engineering; Massachusetts Institute of Technology. Research Laboratory of ElectronicsJournal
Physical Review Letters
Publisher
American Physical Society
Citation
Gilyén, András, Lloyd, Seth, Marvian, Iman, Quek, Yihui and Wilde, Mark M. 2022. "Quantum Algorithm for Petz Recovery Channels and Pretty Good Measurements." Physical Review Letters, 128 (22).
Version: Final published version
ISSN
0031-9007
1079-7114
Keywords
General Physics and Astronomy