  We argue that a complete characterisation of quantum correlations in
bipartite systems of many dimensions may require a quantity which, even for
pure states, does not reduce to a single number. Subsequently, we introduce
multi-dimensional generalizations of concurrence and find evidence that they
may provide useful tools for the analysis of quantum correlations in mixed
bipartite states. We also introudce {\it biconcurrence} that leads to a
necessary and sufficient condition for separability.
