  Gribov's observation that global gauge fixing is impossible has led to
suggestions that there may be a deep connection between gauge-fixing and
confinement. We find an unexpected relation between the topological
non-triviality of the gauge bundle and coloured states in $SU(N)$ Yang-Mills
theory, and show that such states are necessarily impure. We approximate QCD by
a rectangular matrix model that captures the essential topological features of
the gauge bundle, and demonstrate the impure nature of coloured states
explicitly. Our matrix model also allows the inclusion of the QCD
$\theta$-term, as well as to perform explicit computations of low-lying
glueball masses. This mass spectrum is gapped.
  Since an impure state cannot evolve to a pure one by a unitary
transformation, our result shows that the solution to the confinement problem
in pure QCD is fundamentally quantum information-theoretic.
