Symmetric informationally complete measurements: Can we make big ones out of small ones?

          @misc{ scivideos_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 for Theoretical Physics},
            year = {2009},
            month = {dec},
            note = {PIRSA:09120023 see, \url{https://scivideos.org/index.php/pirsa/09120023}}
          }
          

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.