non-Gaussian noise spectroscopy techniques designed for classical noise sources [@Viola2016; @Oliver2019; @RBLiu2019]; one does not have to decide in advance whether the noise is classical or quantum to perform the characterization. Note that a recent work presented a method to measure arbitrary quantum bath correlation functions [@RBLiu2019]; in contrast, our work focuses on characterizing the most physically-relevant correlation function at each order and identifying a corresponding quasiprobability.

To highlight the utility of our approach, we apply it to the concrete but non-trivial case of photon shot noise in a driven-damped bosonic mode (a relevant source of dephasing noise in circuit QED systems [@Schoelkopf2006; @Devoret2019] among others). Prior work used the Keldysh approach to study this noise at zero frequency [@Clerk2011; @Clerk2016]; here we instead focus on the behaviour of the frequency-resolved third cumulant, the “quantum bispectrum" (QBS). We show that the QBS reveals important new physics and distinct quantum signatures: at low temperatures, qualitatively new features emerge that would never be present in a classical model with only thermal fluctuations. We also show that the QBS is a generic tool for revealing the breaking of detailed balance and violation of Onsager-like symmetry relations. We find that the photon shot noise 