Alladi Ramakrishnan Hall

Pseudo-complexity of purification in free scalar field theories

Sabyasachi Maulik

Saha Institute of Nuclear Physics

Recently a generalization of entanglement entropy was proposed
by replacing the usual density matrix with a transition matrix. This new
quantity is dubbed the 'pseudo entropy'. We borrow this idea and attempt to
define a generalized notion of quantum complexity. We consider a reduced
quantum system and purify it by doubling its degrees of freedom. We then
find the transition matrix for Gaussian states in the enlarged system and
use this to define the 'pseudo-complexity of purification'. We numerically
study the 'pseudo-complexity of purification' in a free scalar field theory
with arbitrary dynamical exponent and compare it with the usual complexity
of purification.