  The state of a finite-dimensional quantum system is described by a density
matrix that can be decomposed into a real diagonal, a real off-diagonal and and
an imaginary off-diagonal part. The latter plays a peculiar role. While it is
intuitively clear that some of the imaginary coordinates cannot have the same
extension as their real counterparts the precise relation is not obvious. We
give a complete characterization of the constraints in terms of tight
inequalities for real and imaginary Bloch-type coordinates. Our description
entails a three-dimensional Bloch ball-type model for the state space. We
uncover a surprising qualitative difference for the state-space boundaries in
even and odd dimensions.
