ABSTRACT:
We give a constructive proof that all mixed states of *N* qubits in
a sufficiently small neighborhood of the maximally mixed state are
separable (unentangled). 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. The bounds show
that no entanglement appears in the physical states at any stage of present
NMR experiments. Though this result raises questions about NMR quantum
computation, further analysis would be necessary to assess the power of
the general unitary transformations, which are indeed implemented in
these experiments, in their action on separable states.