  The universal quantum homogeniser can transform a qubit from any state to any
other state with arbitrary accuracy, using only unitary transformations to
perform this task. Here we present an implementation of a finite quantum
homogeniser using nuclear magnetic resonance (NMR), with a four-qubit system.
We compare the homogenisation of a mixed state to a pure state, and the reverse
process. After accounting for the effects of decoherence in the system, we find
the experimental results to be consistent with the theoretical symmetry in how
the qubit states evolve in the two cases. We analyse the implications of this
symmetry by interpreting the homogeniser as a physical implementation of pure
state preparation and information scrambling.
