  On this PhD thesis we cover the results contained in arXiv:2001.07050,
arXiv:2111.10096 and arXiv:2011.02822, while providing further details about
their derivations.
  In the first two papers, we study the generation and detection of entangled
non-Gaussian states of microwave radiation. These states are produced in a new
parametric oscillator, built recently within the field of cQED, capable of
down-converting a microwave tone into three different tones at once. These
three photons share among their magnitudes quantum correlations, in particular
genuine entanglement. In this text we refer to it as non-Gaussian because of
its manifestation on statistical moments higher than covariances, and we
propose a simple and practical criterion for the design of witnesses capable of
detecting it: they must be built from higher statistical moments that change
through time. Additionally, we speculate on the theoretical implications of the
criterion and find suggestive connections to other entanglement classes, such
as the paradigmatic nonequivalent GHZ and W three qubit states.
  In the third paper, we explore one of the possible applications of quantum
technologies: analog simulation of quantum systems. The literature prior to
this thesis showcases multiple examples of superconducting circuits capable of
mimicking systems in which one must consider both quantum and relativistic
phenomena, such as the dynamical Casimir and Unruh effects. This work explores
the information that can be obtained through analog simulation, proposing a
circuit capable of featuring the internal dynamics of a mirror experiencing a
relativistic trajectory, that is, a mirror producing the dynamical Casimir
effect.
