Title: Algebraic formulations of Zauner's conjectureSpeaker: Jon Yard Affiliation: University of Waterloo Zoom: Please email Emma Watson
Tight complex projective 2-designs are simultaneously maximal sets of equiangular lines and minimal complex projective 2-designs. In quantum information theory, they define optimal measurements known as SIC-POVMs (Symmetric Informationally Complete Positive Operator-Valued Measures). They are conjectured by Zauner to exist in every dimension, even as specific group orbits. Yet, they have only so far been proven to exist in a finite-but-growing list of dimensions via exact, explicit constructions over increasingly high-degree number fields, since identified as specific class fields of real quadratic number fields.