Tensor decompositions with applications to LU and SLOCC equivalence of multipartite pure states

Series
Algebra Seminar
Time
Monday, January 27, 2025 - 1:00pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ian Tan – Auburn University
Organizer
Changxin Ding

Please Note: There will be a pre-seminar at 10:55 am in Skiles 005.

We introduce a broad lemma, one consequence of which is the higher order singular value decomposition (HOSVD) of tensors defined by DeLathauwer, DeMoor and Vandewalle (2000). By an analogous application of the lemma, we find a complex orthogonal version of the HOSVD. Kraus's (2010) algorithm used the HOSVD to compute normal forms of almost all n-qubit pure states under the action of the local unitary group. Taking advantage of the double cover SL2(C)×SL2(C)→SO4(C) , we produce similar algorithms (distinguished by the parity of n) that compute normal forms for almost all n-qubit pure states under the action of the SLOCC group.