  Spread complexity measures the minimized spread of quantum states over all
choices of basis. It generalizes Krylov operator complexity to quantum states
under continuous Hamiltonian evolution. In this paper, we study spread
complexity in the context of high-energy astrophysical neutrinos and propose a
new flavor ratio based on complexity. Our findings indicate that our proposal
might favor an initial ratio of fluxes as $\phi_{\nu_e}^0: \phi_{\nu_\mu}^0:
\phi_{\nu_\tau}^0 = 1:0:0$ over a more generally expected ratio of $1:2:0$,
when the IceCube neutrino observatory achieves its projected sensitivity to
discriminate between flavors. Additionally, complexity-based definitions of
flavor ratios exhibit a slight but nonzero sensitivity to the neutrino mass
ordering, which traditional flavor ratios cannot capture.
