The controlled SWAP test for determining quantum entanglement

Abstract

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 useful 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 that the concurrence of a two-qubit state is related to the test's output probabilities. We also propose a multipartite measure of entanglement that acts similarly for n-qubit states. The number of copies required to detect entanglement decreases for larger systems, to four on average for many (n>8) qubits for maximally entangled states. For non-maximally entangled states, the average number of copies of the test state required to detect entanglement increases with decreasing entanglement. Furthermore, the results are robust to second order when typical small errors are introduced to the state under investigation.

arXiv comment17 pages (+ 6 pages references and appendix), 15 figures. To be published in Quantum Science and Technology

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• Multipartite entanglement measures via Bell basis measurements
• Swap Test-based Characterization of Quantum Processes in Universal Quantum Computers
• A Hierarchy of Multipartite Correlations Based on Concentratable Entanglement
• Cross-Platform Verification in Quantum Networks
• Generalising multipartite concentratable entanglement for practical applications: mixed, qudit, and optical states
• Quantum clustering and jet reconstruction at the LHC