PIRSA:19020069

Numerical decomposition of finite dimensional group representations

Rosset, D. (2019). Numerical decomposition of finite dimensional group representations. Perimeter Institute. https://pirsa.org/19020069

Rosset, Denis. Numerical decomposition of finite dimensional group representations. Perimeter Institute, Feb. 13, 2019, https://pirsa.org/19020069 

          @misc{ pirsa_PIRSA:19020069,
            doi = {10.48660/19020069},
            url = {https://pirsa.org/19020069},
            author = {Rosset, Denis},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Numerical decomposition of finite dimensional group representations},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {feb},
            note = {PIRSA:19020069 see, \url{https://pirsa.org}}
          }

Denis Rosset Perimeter Institute for Theoretical Physics

DOI 10.48660/19020069
Collection
Talk Type Scientific Series
Subject

Abstract

Group representations are ubiquitous in quantum information theory. Many important states or channels are invariant under particular symmetries: for example depolarizing channels, Werner states, isotropic states, GHZ states. Accordingly, computations involving those objects can be simplified by invoking the symmetries of the problem. For that purpose, we need to know which irreducible representations appear in the problem, and how. Decomposing a representation is a hard problem; however, we can cheat and use numerical techniques to approximate the change of basis matrix -- and even recover exact results.