The representation theory of Clifford tensor-powers, from Howe to How
PIRSA ID:
19090101
Series:
Quantum Foundations
Event Type:
Seminar
Scientific Area(s):
Quantum Foundations
End date:
Speaker(s):
- Felipe Montealegre, Universität zu Köln
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.