PIRSA:20100030

Video URL

https://pirsa.org/20100030

Quantum algorithms for the Petz recovery channel, pretty-good measurements and polar decomposition

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

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

          @misc{ scivideos_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 for Theoretical Physics},
            year = {2020},
            month = {oct},
            note = {PIRSA:20100030 see, \url{https://scivideos.org/index.php/pirsa/20100030}}
          }

Yihui Quek Massachusetts Institute of Technology (MIT)

Talk numberPIRSA:20100030
DOI10.48660/20100030
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

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.