  Quantum discord characterizes "non-classicality" of correlations in quantum
mechanics. It has been proposed as the key resource present in certain quantum
communication tasks and quantum computational models without containing much
entanglement. We obtain a necessary and sufficient condition for the existence
of non-zero quantum discord for any dimensional bipartite states. This
condition is easily experimentally implementable. Based on this, we propose a
geometrical way of quantifying quantum discord. For two qubits this results in
a closed form of expression for discord. We apply our results to the model of
deterministic quantum computation with one qubit, showing that quantum discord
is unlikely to be the reason behind its speedup.
