  We study the problem of minimizing the energy function $M^p(m,n) := \min
\sum_{1\le i<j\le m} |\langle v_i, v_j\rangle|^p$, where $v_i$ are unit vectors
in $F^n$, $F=\mathbb R$ or $\mathbb C$, $m,n,p>0$ are integers and $p$ is even.
This problem has implications on finding nice polyhedra in projective spaces,
and on quantum random access codes. We conduct experimental search in the
complex case which suggests nice patterns on the minimum values. In some
cases($p=2$ and partially $n=2$) we supply analytical proofs and give full
descriptions of the minimal configurations. We also show that as $m\to \infty$,
nearly equidistributed configurations points nearly give the minimal values we
expect from our patterns.
