Speaker: Ian Tan (Auburn)

 

Title: Tensor factorizations and orbit classification

 

 

Abstract: We introduce a general framework for obtaining tensor factorizations with respect to various group actions. Our motivation comes from orbit classification problems that arise in quantum information. For example, the singular value decomposition gives real diagonal normal forms under left and right multiplication by unitary matrices. Similarly, the higher order singular value decomposition of De Lathauwer et al. was used by B. Kraus to find normal forms for generic n-qubit tensors under the action of the local unitary group. Our perspective explains these tensor factorizations and gives new ones for the "local" special orthogonal group and for the group of Stochastic Local Operations with Classical Communication (SLOCC). Consequently, we obtain SLOCC normal forms for generic n-qubit tensors.

 

This is joint work with Luke Oeding.