  Generic scaling laws, such as the Kolmogorov's 5/3-law, are milestone
achievements of turbulence research in classical fluids. For quantum fluids
such as atomic Bose-Einstein condensates, superfluid helium, and superfluid
neutron stars, turbulence can also exist in the presence of a chaotic tangle of
evolving quantized vortex lines. However, due to the lack of suitable
experimental tools to directly probe the vortex-tangle motion, so far little is
known about possible scaling laws that characterize the velocity correlations
and trajectory statistics of the vortices in quantum-fluid turbulence (QT).
Acquiring such knowledge could greatly benefit the development of advanced
statistical models of QT. Here we report an experiment where a tangle of
vortices in superfluid $^4$He are decorated with solidified deuterium tracer
particles. Under experimental conditions where these tracers follow the motion
of the vortices, we observed an apparent superdiffusion of the vortices. Our
analysis shows that this superdiffusion is not due to L\'{e}vy flights, i.e.,
long-distance hops that are known to be responsible for superdiffusion of
random walkers. Instead, a previously unknown power-law scaling of the
vortex-velocity temporal correlation is uncovered as the cause. This finding
may motivate future research on hidden scaling laws in QT.
