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The "Power of One Qubit" refers to a computational model that has access toonly one pure bit of quantum information, along with n qubits in the totallymixed state. This model, though not as powerful as a pure-state quantumcomputer, is capable of performing some computational tasks exponentiallyfaster than any known classical algorithm. One such task is to estimate withfixed accuracy the normalized trace of a unitary operator that can beimplemented efficiently in a quantum circuit. We show that circuits of thistype generally lead to entangled states, and we investigate the amount ofentanglement possible in such circuits, as measured by the multiplicativenegativity. We show that the multiplicative negativity is bounded by aconstant, independent of n, for all bipartite divisions of the n+1 qubits, andso becomes, when n is large, a vanishingly small fraction of the maximumpossible multiplicative negativity for roughly equal divisions. This suggeststhat the global nature of entanglement is a more important resource for quantumcomputation than the magnitude of the entanglement.Comment: 22 pages, 4 figure

Entanglement and the power of one qubit