bibkey: pauwelsguhne2026measurementbases authors: Jef Pauwels; Otfried Gühne year: 2026 title: “The Entanglement Content of Quantum Measurement Bases” doi: null url: https://arxiv.org/abs/2608.21185v1 claim: “Four-qubit marginal entropy: the Higuchi–Sudbery candidate, its known restrictions, and the unrestricted maximum question.” strata_touched:

• D5/S3/Quantum/Entanglement/HiguchiSudbery/HiguchiSudberyEntropyMaximum license: citation-only triage: anchor

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Source: https://arxiv.org/abs/2608.21185v1

The Entanglement Content of Quantum Measurement Bases

Status of global optimality

Section IV, p. 8:

Higuchi and Sudbery originally proposed it using the corresponding average von Neumann entropy; it is a proven local maximum and a global maximum within the 1-uniform family for that functional, while unrestricted global optimality remains conjectural [34, 36, 46].

The preceding sentences distinguish this functional from two established maxima:

The example is independently notable for its entanglement. It globally maximizes both the geometric measure [35, 45] and the average two-versus-two linear entropy [36].

The displayed state has $\omega =e^{2\pi i/3}$ and the same six occupied computational basis strings as the original Higuchi–Sudbery candidate. This note attests the published open status of the unrestricted average von Neumann entropy question; it supplies no proof of the entropy bound.