The controlled SWAP test for determining quantum entanglement

Quantum entanglement is essential to the development of quantum computation, communications and technology. The controlled SWAP test, widely used for state comparison, can be adapted to an efficient and general test for entanglement of a pure state. Here we show that the test can evidence the presence of entanglement (and further, genuine $n$-qubit entanglement), can distinguish entanglement classes, and generates the concurrence in the case of a 2-qubit state. We also propose a multipartite degree of entanglement, related to the test's probability outputs. The average number of measurements required to detect entanglement increases with decreased entanglement. Maximally entangled states require fewer measurements the larger the system, two on average for eight or more qubits. Furthermore, the results are robust to second order when typical small errors are introduced to the state under investigation.