PIRSA:19090101 Scientific Series Quantum Foundations

DOI10.48660/19090101

Series: Quantum Foundations

Montealegre, F. (2019). The representation theory of Clifford tensor-powers, from Howe to How. Perimeter Institute. https://pirsa.org/19090101

Montealegre, Felipe. The representation theory of Clifford tensor-powers, from Howe to How. Perimeter Institute, Sep. 12, 2019, https://pirsa.org/19090101 

@misc{ pirsa_PIRSA:19090101,
  doi = {10.48660/19090101},
  url = {https://pirsa.org/19090101},
  author = {Montealegre, Felipe},
  keywords = {Quantum Foundations},
  language = {en},
  title = {The representation theory of Clifford tensor-powers, from Howe to How},
  publisher = {Perimeter Institute},
  year = {2019},
  month = {sep},
  note = {PIRSA:19090101 see, \url{https://pirsa.org}}
}

Abstract

Schur-Weyl duality, arising from tensor-power representations of the unitary group, is a big useful hammer in the quantum information toolbox. This is especially the case for problems which have a full unitary invariance, say, estimating the spectrum of a quantum state from a few copies. Many problems in quantum computing have a smaller symmetry group: the Clifford group. This talk will show how to decompose tensor-power Clifford representations through a Schur-Weyl type construction. Our results are also relevant for the theory of Howe duality between symplectic and orthogonal groups.

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