Optimizing for an arbitrary Schrödinger cat state. II. Application in the presence of dissipation

We extend here the optimization functional targeting arbitrary cat states, derived in the companion paper, to open quantum system dynamics. Applying it to a Jaynes-Cummings model with decay on the oscillator, we find, for strong dissipation and large cat radii, a change in the control strategy for preparing an entangled cat state. Our results illustrate the versatility of the quantum optimal control toolbox for practical applications in the quantum technologies.