  The "Power of One Qubit" refers to a computational model that has access to
only one pure bit of quantum information, along with n qubits in the totally
mixed state. This model, though not as powerful as a pure-state quantum
computer, is capable of performing some computational tasks exponentially
faster than any known classical algorithm. One such task is to estimate with
fixed accuracy the normalized trace of a unitary operator that can be
implemented efficiently in a quantum circuit. We show that circuits of this
type generally lead to entangled states, and we investigate the amount of
entanglement possible in such circuits, as measured by the multiplicative
negativity. We show that the multiplicative negativity is bounded by a
constant, independent of n, for all bipartite divisions of the n+1 qubits, and
so becomes, when n is large, a vanishingly small fraction of the maximum
possible multiplicative negativity for roughly equal divisions. This suggests
that the global nature of entanglement is a more important resource for quantum
computation than the magnitude of the entanglement.
