Entangled measurement for W states

Entangled measurements are an indispensable tool for quantum information processing, such as Bell-state measurements in quantum teleportation and entanglement swapping. However, to date, the realization of entangled measurements has mainly focused on bipartite systems or Greenberger-Horne-Zeilinger (GHZ) states. Here, we demonstrate a practical scheme to realize entangled measurements for [Formula: see text] states. Thanks to the cyclic shift symmetry in the discrete Fourier transformation (DFT) of bosonic modes, the DFT measurement outcomes can be used to deterministically project multiqubit states onto [Formula: see text] states. Experimentally, we show that three-qubit [Formula: see text] state discrimination can be achieved by detecting the cyclic shift symmetry with a three-mode DFT optical circuit, yielding a measurement discrimination fidelity of 0.871 ± 0.039. Our experimental demonstration opens the door for the development of new quantum network protocols between multipartite systems.