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. We build on the work of van Dam et al. in their 2008 patent which shows that the 2-qubit c-SWAP test evidences entanglement and details an optical implementation; and Gutoski et al. [Theory Comput. 11: 59, 2015] which proves the product-state c-SWAP test is a complete problem for BQP. Here we show that for any n-qubit pure state, 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 many (n≥8) qubits. Furthermore, the results are robust to second order when typical small errors are introduced to the state under investigation. Details in arXiv:2009.07613