  Understanding whether dissipation in an open quantum system is truly quantum
is a question of both fundamental and practical interest. We consider 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 plays a crucial role: broken time-reversal symmetry
is required for dissipative entanglement generation. Further, simply having
nonzero bath susceptibilities is not enough for the dissipation to be quantum.
We also present an explicit experimental protocol for identifying truly quantum
dephasing dissipation and lay the groundwork for studying more complex
dissipative systems and finding optimal noise mitigating strategies.
