the frequency dependence of this contribution to the bispectrum is the same both in the classical high-temperature limit ${\bar n}_\mathrm{th} \to \infty $, and in the extreme quantum limit ${\bar n}_\mathrm{th} \to 0$; the only temperature dependence is in the prefactor. $S_{\mathrm{th} }   [ {\omega}_{1},{\omega}_{2}  ]$ vanishes in the absence of thermal fluctuations (i.e. ${\bar n}_\mathrm{th} \to 0$). In the limit ${\bar n}_\mathrm{th} \to 0$, this expression corresponds (as expected) to the bispectrum of asymmetric telegraph noise (see e.g., [@Sinitsyn2013]), corresponding to fluctuations between the $n=0$ and $n=1$ Fock states. While our general result here suggests that the $\omega$ dependence of the QBS is not sensitive to quantum corrections, we will see that this is not true as soon as a coherent drive is added to the system.

[*Quantum bispectrum of driven photon-number fluctuations–* ]{} We now consider the drive-dependent contribution to the bispectrum, $S_{\mathrm{dr} }   [ {\omega}_{1},{\omega}_{2}  ]$ in Eq. (\[eq:QBSDecomposition\]). This quantity only depends on the drive amplitude $f$ through the overall prefactor ${\bar n}_{ \rm{dr} } =4 |f|^2/(\gamma^2+ 4\delta^2)$ (the intracavity photon number generated by $f$). Note that $S_{\mathrm{dr} }   [ {\omega}_{1},{\omega}_{2}  ]$ remains non-zero at zero temperature, and is the only contribution to the QBS in 