Quantum Algorithm for Petz Recovery Channels and Pretty Good Measurements
Name
PhysRevLett.128.220502.pdf
Size
230.56 KB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Gilyén, András
Lloyd, Seth
Marvian, Iman
Quek, Yihui
Wilde, Mark M.
Date Issued
June 1, 2022
Journal
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
Abstract
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.
Subjects
General Physics and Astronomy
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Research Laboratory of Electronics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/physrevlett.128.220502
