PIRSA:09120023 Scientific Series Quantum Foundations

DOI10.48660/09120023

Series: Quantum Foundations

Wootters, W. (2009). Symmetric informationally complete measurements: Can we make big ones out of small ones?. Perimeter Institute. https://pirsa.org/09120023

Wootters, William. Symmetric informationally complete measurements: Can we make big ones out of small ones?. Perimeter Institute, Dec. 01, 2009, https://pirsa.org/09120023 

@misc{ pirsa_PIRSA:09120023,
  doi = {10.48660/09120023},
  url = {https://pirsa.org/09120023},
  author = {Wootters, William},
  keywords = {Quantum Foundations},
  language = {en},
  title = {Symmetric informationally complete measurements: Can we make big ones out of small ones?},
  publisher = {Perimeter Institute},
  year = {2009},
  month = {dec},
  note = {PIRSA:09120023 see, \url{https://pirsa.org}}
}

Abstract

For a quantum system with a d-dimensional Hilbert space, a symmetric informationally complete measurement (SIC) can be thought of as a set of d^2 pure states all having the same overlap. Constructions of SICs for composite systems usually do not make use of the composite structure but treat the system as a whole. Indeed for some cases, one can prove that a SIC cannot have the symmetry that one naturally associates with the composite structure. In this talk I give one example showing how a SIC for three qubits can be constructed from SICs for the individual qubits. I ask whether the strategy used in this example might apply to other composite cases.

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