Quantum

A New Non-Affine Family in the Karlsson-Szollosi Intersection

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 27/10/2026, 04:13:24 UTC.

Briefings

A new non-affine family of complex Hadamard matrices was identified in the intersection of two-parameter Hadamard families from Karlsson and Sz\"oll\H{o}si. The study classifies this family using a new parametrisation in Karlsson coordinates and reveals the intersection is strictly larger than the known affine Di\c{t}\u{a} curve. This finding advances the search for mutually unbiased bases in six dimensions.

Key points

• The intersection of the two-parameter Hadamard families of Karlsson and Sz\"oll\H{o}si is strictly larger than the known affine Di\c{t}\u{a} curve $D_6^{(1)}$.
• A new non-affine one-parameter family $C_6^{(1)}$ was identified as part of the intersection, requiring a new parametrisation in Karlsson coordinates.

Context

This research addresses the intersection of block-reducible forms and hypocycloid constraints, potentially supporting the search for mutually unbiased bases in six dimensions.

Limitations

The evidence is a preprint from arXiv:2610.33207v1, indicating it is under review and subject to change. The classification relies on standard Hadamard equivalence and specific coordinate transformations not fully detailed in the abstract.

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