We investigate the generalization of symmetric quantum joint measurements on multiple qubits. We first describe a method for constructing a symmetric joint measurement basis for three qubits by utilizing single-qubit states corresponding to the four vertices of an isohedral tetrahedron on the Bloch sphere. We then demonstrate the expected tetrahedral symmetry of the current measurement basis and discuss its application in a trilocal star-shaped network. This architecture enables us to generalize the two-qubit symmetric joint measurement to an $n$ -qubit version, preserving the tetrahedral or hexahedral symmetry.We investigate the generalization of symmetric quantum joint measurements on multiple qubits. We first describe a method for constructing a symmetric joint measurement basis for three qubits by utilizing single-qubit states corresponding to the four vertices of an isohedral tetrahedron on the Bloch sphere. We then demonstrate the expected tetrahedral symmetry of the current measurement basis and discuss its application in a trilocal star-shaped network. This architecture enables us to generalize the two-qubit symmetric joint measurement to an $n$-qubit version, preserving the tetrahedral or hexahedral symmetry.

arXiv:2503.08993Physical Review AMay 28, 20254 citations

Symmetric joint measurement as a complement to the elegant joint measurement

Ying-Qiu He, Yu-Yan Zhang, Dong Ding +2 more

Traditional Bell state measurement (BSM) and product basis measurements (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 [Phys.Rev.Lett.126:220401], a parameterized two-qubit iso-entangled 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 [Phys.Rev.Lett.126:220401] and contains 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 reduction vectors of the current basis states exhibit rotational symmetry, rather than the aforementioned 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.Traditional Bell state measurement (BSM) and product basis measurements (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 [Phys.Rev.Lett.126:220401], a parameterized two-qubit iso-entangled 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 [Phys.Rev.Lett.126:220401] and contains 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 reduction vectors of the current basis states exhibit rotational symmetry, rather than the aforementioned 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.

quant-pharXiv:2602.04173Physical Review AFeb 5, 20260 citations

Pairwise entanglement in symmetric multi-qubit systems

X. Wang, Klaus Mølmer

arXiv:quant-ph/0106145The European Physical Journal DMar 1, 200264 citations

Quantum entanglement in multi-qubit systems

최정운

Jan 1, 20040 citations

Multiqubit Elegant Joint Measurement

Jef Pauwels, Nicolas Gisin

The elegant joint measurement (EJM) is a highly symmetric, partially entangled two-qubit measurement whose local marginals form a regular tetrahedron on the Bloch sphere and which has a low entanglement cost for local implementation. It plays a central role in quantum networks exhibiting nonclassical correlations and serves as a paradigmatic example of an entangled measurement with local structure. Despite its significance, generalizing the EJM beyond two qubits has remained unresolved. Here, we extend the EJM to the multipartite setting by identifying all tetrahedrally symmetric, efficiently localizable multiqubit bases. For two qubits, these criteria uniquely select the EJM. For three or more, they yield a discrete set of equivalence classes, reflecting the richer structure of multiparticle entanglement.The elegant joint measurement (EJM) is a highly symmetric, partially entangled two-qubit measurement whose local marginals form a regular tetrahedron on the Bloch sphere and which has a low entanglement cost for local implementation. It plays a central role in quantum networks exhibiting nonclassical correlations and serves as a paradigmatic example of an entangled measurement with local structure. Despite its significance, generalizing the EJM beyond two qubits has remained unresolved. Here, we extend the EJM to the multipartite setting by identifying all tetrahedrally symmetric, efficiently localizable multiqubit bases. For two qubits, these criteria uniquely select the EJM. For three or more, they yield a discrete set of equivalence classes, reflecting the richer structure of multiparticle entanglement.

arXiv:2509.01852Physical Review LettersApr 22, 20262 citations

n

-qubit version, preserving the tetrahedral or hexahedral symmetry.