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PreprintCC BY 4.0arXiv

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

  • Wojciech Bruzda
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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 ± 1/√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.

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Cite

BibTeXRIS
BibTeX
@misc{bruzda2026geomagic,
  title = {{Geomagic Square Representation of a Real AME$(4, 6)$ State}},
  author = {Wojciech Bruzda},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16882},
  eprint = {2610.16882},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16882},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Geomagic Square Representation of a Real AME$(4, 6)$ State
AU  - Wojciech Bruzda
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16882
UR  - https://arxiv.org/abs/2610.16882
AB  - 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 ± 1/√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.
ER  -