PIRSA:19110141

The representation theory of the Clifford group, with applications to resource theories

Gross, D. (2019). The representation theory of the Clifford group, with applications to resource theories. Perimeter Institute. https://pirsa.org/19110141

Gross, David. The representation theory of the Clifford group, with applications to resource theories. Perimeter Institute, Nov. 28, 2019, https://pirsa.org/19110141 

          @misc{ pirsa_PIRSA:19110141,
            doi = {10.48660/19110141},
            url = {https://pirsa.org/19110141},
            author = {Gross, David},
            keywords = {Quantum Information},
            language = {en},
            title = {The representation theory of the Clifford group, with applications to resource theories},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {nov},
            note = {PIRSA:19110141 see, \url{https://pirsa.org}}
          }

David Gross

Universität zu Köln

Talk number
PIRSA:19110141
Collection
Talk Type
Subject
Abstract
I will report on an ongoing project to work out and exploit an analogue of Schur-Weyl duality for the Clifford group. Schur-Weyl establishes a one-one correspondence between irreps of the unitary group and those of the symmetric group. A similar program can be carried out for Cliffords. The permutations are then replaced by certain discrete orthogonal maps. As is the case for Schur-Weyl, this duality has many applications for problems in quantum information. It can be used, e.g., to derive quantum property tests for stabilizerness and Cliffordness, a new direct interpretation of the sum-negativity of Wigner functions, bounds on stabilizer rank, the construction of designs using few non-Clifford resources, etc. [arXiv:1609.08172, arXiv:1712.08628, arXiv:1906.07230, arXiv:out.soon].