  Recent discoveries have highlighted the significance of replica wormholes in
resolving the information paradox and establishing the unitarity of black hole
evaporation. In this letter, we propose the dissipative Sachdev-Ye-Kitaev model
(SYK) as a minimal quantum model that exhibits entanglement dynamics with
features qualitatively similar to replica wormholes. As a demonstration, we
investigate the entanglement growth of a pair of dissipative SYK models
initialized in a thermofield double state (TFD). In the regime of large $N$
with weak dissipation, we observe a first-order entanglement transition
characterized by a switch of the dominant saddle point: from replica diagonal
solutions for short times to replica wormhole-like off-diagonal solutions for
long times. Furthermore, we show that signature of replica wormholes persists
even at moderate $N \lesssim 30$ by using the Monte Carlo quantum trajectory
method. Our work paves the way for explorations of replica wormhole physics in
quantum simulators.
