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≥5 we do not know an analogous closed-form family. We also give an analogous construction, valid for every n ≥3, with square local geometry.
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BibTeX
@misc{pauwels2026tunable,
title = {{Tunable Families of Multiqubit Elegant Joint Measurements}},
author = {Jef Pauwels and Nicolas Gisin},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.16020},
eprint = {2607.16020},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.16020},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Tunable Families of Multiqubit Elegant Joint Measurements
AU - Jef Pauwels
AU - Nicolas Gisin
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2607.16020
UR - https://arxiv.org/abs/2607.16020
AB - 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≥5 we do not know an analogous closed-form family. We also give an analogous construction, valid for every n ≥3, with square local geometry.
ER -