Our first talks will be on April 7 (Thursday 12 noon, virtual, speaker from Europe) and 8 (in person in Fort Collins).

https://zoom.us/j/95321487441?pwd=Tlp4VG9pejZCekJmeDFFb1BzeWpsdz09
Meeting ID: 953 2148 7441
Passcode: 722523

Willen De Graaf – U. Trento, Italy

Title: Classification of four qubit and rebit states

Abstract: We consider the problem of classifying the orbits of $\mbox{SL}(2,{\mathbb{C}})^4$ on
the space ${\mathbb{C}}^2\otimes {\mathbb{C}}^2\otimes {\mathbb{C}}^2\otimes {\mathbb{C}}^2$. In quantum information
theory this is known as the classification of four qubit states under
SLOCC operations. We approach the problem by constructing the representation
via a symmetric pair of maximal rank. This makes it possible to apply the
theory of $\theta$-representations developed by Vinberg in the 70’s.
The orbits are devided into three types: nilpotent, semisimple and mixed.
The orbits of each type are classified separately. We also obtain the
stabilizers of representatives of the orbits. The talk will end with
some comments on the same problem over $\R$, known as the classification
of four rebit states. This is joint work with Heiko Dietrich, Alessio
Marrani and Marcos Origlia.