Understanding whether dissipation in an open quantum system is truly quantum is a question of both fundamental and practical interest. We consider a general model of n qubits subject to correlated Markovian dephasing, and present a sufficient condition for when bath-induced dissipation can generate system entanglement and hence must be considered quantum. Surprisingly, we find that the presence or absence of time-reversal symmetry (TRS) plays a crucial role: broken TRS is required for dissipative entanglement generation. Further, simply having non-zero bath susceptibilities is not enough for the dissipation to be quantum. Our work also present an explicit experimental protocol for identifying truly quantum dephasing dissipation, and lays the groundwork for studying more complex dissipative systems and finding optimal noise mitigating strategies.
