  We establish a rigorous connection between quantum coherence and quantum
chaos by employing coherence measures originating from the resource theory
framework as a diagnostic tool for quantum chaos. We quantify this connection
at two different levels: quantum states and quantum channels. At the level of
states, we show how several well-studied quantifiers of chaos are, in fact,
quantum coherence measures in disguise (or closely related to them). We further
this connection for all quantum coherence measures by using tools from
majorization theory. Then, we numerically study the coherence of
chaotic-vs-integrable eigenstates and find excellent agreement with random
matrix theory in the bulk of the spectrum. At the level of channels, we show
that the coherence-generating power (CGP) -- a measure of how much coherence a
dynamical process generates on average -- emerges as a subpart of the
out-of-time-ordered correlator (OTOC), a measure of information scrambling in
many-body systems. Via numerical simulations of the (nonintegrable)
transverse-field Ising model, we show that the OTOC and CGP capture quantum
recurrences in quantitatively the same way. Moreover, using random matrix
theory, we analytically characterize the CGP-OTOC connection for the Haar and
Gaussian ensembles. In closing, we remark on how our coherence-based signatures
of chaos relate to other diagnostics, namely the Loschmidt echo, OTOC, and the
Spectral Form Factor.
