  We give a constructive proof that all mixed states of N qubits in a
sufficiently small neighborhood of the maximally mixed state are separable. The
construction provides an explicit representation of any such state as a mixture
of product states. We give upper and lower bounds on the size of the
neighborhood, which show that its extent decreases exponentially with the
number of qubits. We also discuss the implications of the bounds for NMR
quantum computing.
