PIRSA:20100030 Scientific Series Quantum Information

DOI10.48660/20100030

Series: Perimeter Institute Quantum Discussions

Quek, Y. (2020). Quantum algorithms for the Petz recovery channel, pretty-good measurements and polar decomposition. Perimeter Institute. https://pirsa.org/20100030

Quek, Yihui. Quantum algorithms for the Petz recovery channel, pretty-good measurements and polar decomposition. Perimeter Institute, Oct. 07, 2020, https://pirsa.org/20100030 

@misc{ pirsa_PIRSA:20100030,
  doi = {10.48660/20100030},
  url = {https://pirsa.org/20100030},
  author = {Quek, Yihui},
  keywords = {Quantum Information},
  language = {en},
  title = {Quantum algorithms for the Petz recovery channel, pretty-good measurements and polar decomposition},
  publisher = {Perimeter Institute},
  year = {2020},
  month = {oct},
  note = {PIRSA:20100030 see, \url{https://pirsa.org}}
}

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. We rectify this lack using the recently developed tools of quantum singular value transformation and oblivious amplitude amplification, providing a quantum algorithm to implement the Petz recovery channel. 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.

Using the same toolbox, we also develop a quantum algorithm for enacting the polar decomposition, a workhorse in linear algebra. This provides an alternative route to implementing a pretty-good measurements for the special case of pure states, which speeds up the general-purpose algorithm developed above.

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