  The non-commutative nature of quantum mechanics imposes fundamental
constraints on system dynamics, which in the linear realm are manifested by the
physical realizability conditions on system matrices. These restrictions endow
system matrices with special structure. The purpose of this paper is to study
such structure by investigating zeros and poses of linear quantum systems. In
particular, we show that $-s_0^\ast$ is a transmission zero if and only if
$s_0$ is a pole, and which is further generalized to the relationship between
system eigenvalues and invariant zeros. Additionally, we study
left-invertibility and fundamental tradeoff for linear quantum systems in terms
of their zeros and poles.
