Generalizing multipartite concentratable entanglement for practical applications: mixed, qudit and optical states.

The controlled SWAP test for detecting and quantifying entanglement applied to pure qubit states is robust to small errors in the states and efficient for large multi-qubit states (Foulds . 2021 . , 035002 (doi:10.1088/2058-9565/abe458)). We extend this, and the related measure (CE), to enable important practical applications in quantum information processing. We investigate the lower bound of concentratable entanglement given in (Beckey . 2023 , 062425 (doi:10.1103/physreva.107.062425)) and conjecture an upper bound of the mixed-state concentratable entanglement that is robust to c-SWAP test errors. Since experimental states are always slightly mixed, our work makes the c-SWAP test and CE measure suitable for application in experiments to characterize entanglement. We further present the CE of some key higher-dimensional states such as qudit states and entangled optical states to validate the CE as a higher-dimensional measure of entanglement.This article is part of the theme issue 'The quantum theory of light'.