  We establish a statistical relationship between the inverse energy cascade
and the spatial correlations of clustered vortices in two-dimensional quantum
turbulence. The Kolmogorov spectrum $k^{-5/3}$ on inertial scales $r$
corresponds to a pair correlation function between the vortices with different
signs that decays as a power law with the pair distance given as $r^{-4/3}$. To
test these scaling relations, we propose a novel forced and dissipative point
vortex model that captures the turbulent dynamics of quantized vortices by the
emergent clustering of same-sign vortices. The inverse energy cascade
developing in a statistically neutral system originates from this vortex
clustering that evolves with time.
