Traditional Bell state measurement (BSM) and the product basis measurement (PBM) have been integral to nearly the entire development of quantum computing. Unlike the BSM and the PBM, a recently proposed two-qubit joint measurement called the elegant joint measurement (EJM) exhibits novel tetrahedral symmetry in its single-qubit reduced states. In Tavakoli et al. [Phys. Rev. Lett. 126, 220401 (2021)], a parametrized two-qubit isoentangled basis was proposed, with concurrence between 1/2 and 1, perfectly spanning the original EJM and conventional BSM. We present a two-qubit symmetric joint measurement having concurrence from 0 to 1/2, which is complementary to the parametrized EJM and connects the PBM and the original EJM. We investigate the symmetry of the current structure and its application in triangular networks. The results indicate that the reduced vectors of the current basis states exhibit rotational symmetry rather than mirror symmetry; moreover, the output probability distributions of three parties in the network explicitly demonstrate the expected permutation symmetry. Furthermore, we generalize the two-qubit symmetric joint measurement to the multiqubit systems with an even number of qubits.

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• Quantum information processing