PIRSA:07100033 Scientific Series Quantum Information

DOI10.48660/07100033

Series: Perimeter Institute Quantum Discussions

Boileau, J.C. (2007). Quantum Reference Frames and the Classification of Rotationally-Invariant Maps. Perimeter Institute. https://pirsa.org/07100033

Boileau, Jean Christian. Quantum Reference Frames and the Classification of Rotationally-Invariant Maps. Perimeter Institute, Oct. 24, 2007, https://pirsa.org/07100033 

@misc{ pirsa_PIRSA:07100033,
  doi = {10.48660/07100033},
  url = {https://pirsa.org/07100033},
  author = {Boileau, Jean Christian},
  keywords = {Quantum Information},
  language = {en},
  title = {Quantum Reference Frames and the Classification of Rotationally-Invariant Maps},
  publisher = {Perimeter Institute},
  year = {2007},
  month = {oct},
  note = {PIRSA:07100033 see, \url{https://pirsa.org}}
}

Abstract

We give a convenient representation for any map which is covariant with respect to an irreducible representation of SU(2), and use this representation to analyze the evolution of a quantum directional reference frame when it is exploited as a resource for performing quantum operations. We introduce the moments of a quantum reference frame, which serve as a complete description of its properties as a frame, and investigate how many times a quantum directional reference frame represented by a spin-j system can be used to perform a certain quantum operation with a given probability of success. We provide a considerable generalization of previous results on degradation of reference frame, from which follows a classification of the dynamics of spin-j system under the repeated action of any covariant map with respect to SU(2). Joint work with Lana Sheridan, Martin Laforest and Stephen Bartlett

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