Symmetric Informationally Complete Positive Operator Valued Measures (SIC-POVMs) and Mutually Unbiased Bases (MUBs), their possible relations, geometric and entropic properties.
Our research has mainly been on identifying the geometric and entropic properties of SIC-POVMs and MUBs. SIC-POVMs are equiangular vectors in Hilbert space and they are believed to exist in any dimension (Zauner’s conjecture). Our interest is determining the structural properties of known SIC-POVM solutions. We are also examining the informational relations between different SIC-POVMs by using entropic methods. Our results have applications in Quantum Bayesianism (QBism).