Frame Potential in CPⁿ Some Numerical and Analytical Results

Abstract

In this paper we discuss minimizing a generalized frame potential - F(p,m,n) - for vectors in CPⁿ. We discuss the minimal frame potential as well as the space of solutions for the minimization problem. We investigate this question both numerically and analytically. We find that for some values of p - Equiangular Tight Frames (ETF) are unique solutions, in contrast to the case of p = 2 where they are non-unique solutions.

Keywords:

• Energy minimization
• CPn
• frame potential
• equiangular tight frame

Declaration of interest

No potential conflict of interest was reported by the author(s).