QLunch : Benjamin Lovitz

Speaker: Benjamin Lovitz. University of Waterloo

Title: A splitting theorem for product tensors

Abstract: Tensors are natural generalizations of matrices to higher-way arrays. Decompositions of tensors into sums of product (rank-one) tensors are useful in many areas for compressing and interpreting data. In this talk, I will describe a splitting theorem for sets of product tensors, a corollarial generalization of Kruskal's theorem on uniqueness of tensor rank decompositions, and an application in algebraic statistics. As quantum-ish applications of the splitting theorem, we will analyze the sets of product tensors that appear in the canonical decompositions of the W and GHZ states, and study absolutely entangled sets of states. Based on arXiv:1812.01449 and arXiv:2103.15633. The latter is joint work with Fedor Petrov.