Quantum Information Seminar | November 20, 10:30
Positive maps and matrix contractions from the symmetric group
The study of polynomials that are positive on certain sets has a rich history, going back to Hilbert's seventeenth problem. Here we will look at multivariate polynomials (and more generally, tensor contractions) that have matrices as their variables. We present a family of maps that are positive semi-definite on the positive cone. This extends the well-known concept of positive maps as used in entanglement theory to the multilinear case. We will present connections to polynomial identity rings and central polynomials, concepts that found recent use in quantum information in the context of MPS bond dimension witnesses and remote time manipulation.
Felix Huber, ICFO, Barcelona
Seminar Room 0.03, ETP
Contact: David Gross