A new construction of approximately SIC-POVMs derived from Jacobi sums over finite fields

Abstract

In quantum information theory, symmetric informationally complete positive operator-valued measures (SIC-POVMs) are related to quantum state tomography, quantum cryptography and foundational studies. However, constructing SIC-POVMs is notoriously hard. Although some SIC-POVMs have been constructed numerically, there does not exist an infinite family of them until now. In this paper, we utilize Jacobi sums over finite fields to propose a construction of approximately SIC-POVMs. The dimension of this approximately SIC-POVMs is $$q-2$$ , where q is a prime power. Notably, the dimension of the obtained approximately SIC-POVM from our framework is new.