Tunable Families of Multiqubit Elegant Joint Measurements

Abstract:We give a closed-form construction of the $n$-qubit Elegant Joint Measurement (EJM) proposed in [PRL \textbf{136}, 190201 (2026)] and show that it is part of a tunable family of measurements with tetrahedrally arranged Bloch vectors. The construction is based on the interference pattern implied by a single phase polynomial built from the elementary symmetric functions. It realises a regular tetrahedral measurement for every $n$, and the corresponding measurement unitary lies at level $n{+}1$ of the Clifford hierarchy. Starting from this measurement, we ask whether the size of the local tetrahedron -- and hence the entanglement of the basis -- can be varied while preserving its symmetry. For every even $n$ the answer is yes, and remarkably the size follows the same one-parameter law that governs the known two-qubit family, interpolating down to a $1$-uniform basis. For $n=3$ the EJM is locally isolated, while for odd $n\ge5$ we do not know an analogous closed-form family. We also give an analogous construction, valid for every $n \geq3$, with square local geometry.

arXiv:2607.16020 [quant-ph]

(or arXiv:2607.16020v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.16020 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. A 114, L050402 (2026)

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