Geomagic Square Representation of a Real AME$(4,6)$ State

Abstract

Seeking a pictorial representation of four-party absolutely maximally entangled (AME) states of local size six, we independently construct a real AME$(4,6)$ state from a table of signed Pauli matrices. Its two-unitary matrix has $60$ nonzero entries, equal to $1$ or $\pm 1/\sqrt{2}$. A locally equivalent representative yields a genuine geomagic square, where every row, column and main diagonal tiles a hexagon and all $36$ pieces are pairwise non-congruent. Colors, shapes and hatching retain the full tensor, allowing its reconstruction from the picture.

arXiv comment6 pages, 2 figures, 1 table. Scripts and data: https://github.com/matrix-toolbox/AME_4_6