  Having accurate tools to describe non-classical, non-Gaussian environmental
fluctuations is crucial for designing effective quantum control protocols and
understanding the physics of underlying quantum dissipative environments. We
show how the Keldysh approach to quantum noise characterization can be usefully
employed to characterize frequency-dependent noise, focusing on the quantum
bispectrum (i.e., frequency-resolved third cumulant). Using the paradigmatic
example of photon shot noise fluctuations in a driven bosonic mode, we show
that the quantum bispectrum can be a powerful tool for revealing distinctive
non-classical noise properties, including an effective breaking of detailed
balance by quantum fluctuations. The Keldysh-ordered quantum bispectrum can be
directly accessed using existing noise spectroscopy protocols.
