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Q: Fachverband Quantenoptik und Photonik

Q 16: Quantum Information (Concepts and Methods) III

Q 16.6: Vortrag

Dienstag, 10. März 2020, 15:15–15:30, e001

Positive maps and matrix contractions from the symmetric group — •Felix Huber — ICFO Barcelona, Spain

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 on the positive cone. This extends the well-known concept of positive maps as used in entanglement theory to the multilinear case. We present connections to polynomial identity rings as well as central polynomials and show some applications in entanglement detection.