  In classical viscous fluids, turbulent eddies are known to be responsible for
the rapid spreading of embedded particles. But in an inviscid quantum fluid
where the turbulence is induced by a chaotic tangle of quantized vortices,
dispersion of the particles is achieved via a non-classical mechanism, i.e.,
their binding to the evolving quantized vortices. However, there is limited
existing knowledge on how the vortices diffuse and spread in turbulent quantum
fluids. Here we report a systematic numerical study of the apparent diffusion
of vortices in a random vortex tangle in superfluid helium-4 using full
Biot-Savart simulation. We reveal that the vortices in pure superfluid exhibit
a universal anomalous diffusion (superdiffusion) at small times, which transits
to normal diffusion at large times. This behavior is found to be caused by a
generic scaling property of the vortex velocity, which should exist in all
quantum fluids where the Biot-Savart law governs the vortex motion. Our
simulation at finite temperatures also nicely reproduces recent experimental
observations. The knowledge obtained from this study may form the foundation
for understanding turbulent transport and universal vortex dynamics in various
condensed-matter and cosmic quantum fluids.
