  We investigate the properties of natural orbitals and their occupation
numbers of the ground state of two non-interacting anyons characterised by the
fractional statistics parameter $\alpha$ and confined in a harmonic trap. We
work in the boson magnetic gauge where the anyons are modelled as composite
bosons with magnetic flux quanta attached to their positions. We derive an
asymptotic form of the weakly occupied natural orbitals, and show that their
corresponding (ordered descendingly) occupation numbers decay according to the
power law $n^{-(4+2\alpha)}$, where $n$ is the index of the natural orbital. We
find remarkable numerical agreement of the theory with the natural orbitals and
their occupation numbers computed from the spectral decomposition of the
system's wavefunction. We explain that the same results apply to the fermion
magnetic gauge.
