Geomagic Square Representation of a Real AME (4, 6) State
quant-ph
Submitted: 2026-10-12
Updated: 2026-10-12
Comments: 6 pages, 2 figures, 1 table. Scripts and data: https://github.com/matrix-toolbox/AME_4_6
Code: https://github.com/matrix-toolbox/AME_4_6
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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.
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 plus or minus 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.
Sources
- Thirty-six officers, artisanally entangled
- Quantum version of the Euler's problem: a geometric perspective
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