Generalizing the controlled SWAP test for entanglement for practical applications: qudit, optical, and slightly mixed states
The controlled SWAP test for determination of entanglement applied to pure qubit states is both robust to small errors in the states, and efficient for large multi-qubit states [Foulds et al, QST 6 035002, 2021]. We generalize this and similar tests to states with important practical applications in quantum information processing, including higher dimensional (qudit) states, determination of entanglement across a bipartite cut in multi-qubit states, and some key types of entangled optical states, including squeezed states. We show further that the test is robust to a small level of mixedness in the input states, and hence suitable for application in experiments that need to characterize entanglement. We develop a tolerance scheme based on the test's outputs, to quantify confidence levels in the results from tests on imperfect states.