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Quantum entanglement is essential to the development of quantum computation,communications, and technology. The controlled SWAP test, widely used for statecomparison, can be adapted to an efficient and useful test for entanglement ofa pure state. Here we show that the test can evidence the presence ofentanglement (and further, genuine n-qubit entanglement), can distinguishentanglement classes, and that the concurrence of a two-qubit state is relatedto the test's output probabilities. We also propose a multipartite measure ofentanglement that acts similarly for n-qubit states. The number of copiesrequired to detect entanglement decreases for larger systems, to four onaverage for many (n>8) qubits for maximally entangled states. For non-maximallyentangled states, the average number of copies of the test state required todetect entanglement increases with decreasing entanglement. Furthermore, theresults are robust to second order when typical small errors are introduced tothe state under investigation.

The controlled SWAP test for determining quantum entanglement