  We compute the pseudo complexity of purification corresponding to the reduced
transition matrices for free scalar field theories with an arbitrary dynamical
exponent. We plot the behaviour of complexity with various parameters of the
theory under study and compare it with the complexity of purification of the
reduced density matrices of the two states $|\psi_1\rangle$ and
$|\psi_2\rangle$ that constitute the transition matrix. We first find the
transition matrix by reducing to a small number ($1$ and $2$) of degrees of
freedom in lattice from a lattice system with many lattice points and then
purify it by doubling the degrees of freedom ($2$ and $4$ respectively) for
this reduced system. This is a primary step towards the natural extension to
the idea of the complexity of purification for reduced density matrices
relevant for the studies related to post-selection.
