The Multiqubit Elegant Joint Measurement

Abstract

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.

4 + 4 pages, 1 figure. See also companion paper Symmetric Localizable Multipartite Quantum Measurements from Pauli Orbits arXiv:2509.01851, v2: minor improvements

References in corpus (11)

• Entanglement 25 years after Quantum Teleportation: testing joint measurements in quantum networks
• Bilocal Bell inequalities violated by the quantum Elegant Joint Measurement
• Diagonal gates in the Clifford hierarchy
• Entanglement swapping and quantum correlations via Elegant Joint Measurements
• Demonstrating the power of quantum computers, certification of highly entangled measurements and scalable quantum nonlocality
• Bipartite quantum measurements with optimal single-sided distinguishability
• Correspondence between entangled states and entangled bases under local transformations
• Classification of joint quantum measurements based on entanglement cost of localization
• Quantum teleportation based on the elegant joint measurement
• Local encoding of classical information onto quantum states
• Symmetric quantum joint measurements on multiple qubits