Pseudo complexity of purification for free scalar field theories

Abstract

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 twostates|ψ1〉and|ψ2〉that constitute the transition matrix. We reduce to a small number(1 and 2) of degrees of freedom in lattice from a lattice system with many lattice points and purify to double the degrees of freedom (2 and 4 respectively) for the 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.