  Dissipation engineering offers a powerful tool for quantum technologies.
Recently, new superconducting devices demonstrated an engineered two-photon
dissipation rate exceeding all other relevant timescales. In particular, they
have proven most useful to prevent transitions between the logical states
$|\pm\alpha\rangle$ of a cat qubit. Here, we present three key applications of
strong two-photon dissipation for quantum measurement and control, beyond cat
qubit stabilization. Firstly, we demonstrate its efficacy in overcoming
limitations encountered in Wigner tomography at high photon numbers. Secondly,
we showcase its potential for realizing universal gates on cat qubits,
exploiting the coherent mapping between cat qubit states and superpositions of
0 and 1 photons. Finally, we harness the transient dynamics of a cat state
under two-photon dissipation to prepare squeezed cat states with a squeezing
factor exceeding 3.8 dB.
