The representation theory of Clifford tensor-powers, from Howe to How

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.

Collection/Series: 
Event Type: 
Seminar
Scientific Area(s): 
Speaker(s): 
Event Date: 
Thursday, September 12, 2019 - 10:00 to 11:30
Location: 
Sky Room
Room #: 
394