insights into the nature of the underlying dissipative environment.

For classical noise, the frequency-resolved higher noise cumulants (so-called polyspectra [@Rao1984book]) provide a full characterization. Recent work has proposed [@Viola2016; @Ramon2019] and demonstrated [@Oliver2019] measurement protocols to reconstruct polyspectra using a qubit driven by classical non-Gaussian noise. However, the proper generalization of these ideas to truly [*quantum*]{} non-Gaussian noise (as produced by a generic quantum bath) remains an interesting open question; here, the non-commutativity of noise operators at different times poses a challenge as to how best to define polyspectra.

In this paper, we show that the Keldysh approach [@Levitov1996; @Nazarov2003; @BelzigPRL2010; @Clerk2011; @Hofer2017], a method used extensively to characterize low-frequency noise, also provides an unambiguous and practically useful way to describe non-Gaussian quantum bath noise in the frequency domain. It provides a systematic way to construct a quasiprobability distribution to describe the noise, and to assess whether the noise can be faithfully mimicked by completely classical noise processes [@Nazarov2003; @Clerk2011]. It also has a direct operational meaning: the “quantum polyspectra" we introduce are [*exactly*]{} the quantities that contribute to the dephasing of a coupled qubit at each order in the coupling. Moreover, these quantities can be measured using [*the same*]{} 