  Non-Gaussian continuous variable states play a central role both in the
foundations of quantum theory and for emergent quantum technologies. In
particular, "cat states", i.e., two-component macroscopic quantum
superpositions, embody quantum coherence in an accessible way and can be
harnessed for fundamental tests and quantum information tasks alike. Degenerate
optical parametric oscillators can naturally produce single-mode cat states and
thus represent a promising platform for their realization and harnessing. We
show that a dissipative coupling between degenerate optical parametric
oscillators extends this to two-mode entangled cat states, i.e., two-mode
entangled cat states are naturally produced under such dissipative coupling.
While overcoming single-photon loss still represents a major challenge towards
the realization of sufficiently pure single-mode cat states in degenerate
optical parametric oscillators, we show that the generation of two-mode
entangled cat states under such dissipative coupling can then be achieved
without additional hurdles. We numerically explore the parameter regime for the
successful generation of transient two-mode entangled cat states in two
dissipatively coupled degenerate optical parametric oscillators. To certify the
cat-state entanglement, we employ a tailored, variance-based entanglement
criterion, which can robustly detect cat-state entanglement under realistic
conditions.
