Three Quantum Latin Squares of Order 6 with Cardinalities 13, 15, and 17

Zhipeng Xu

Three Quantum Latin Squares of Order 6 with Cardinalities 13, 15, and 17

Combinatorics 2026-05-20 v2

Authors: Zhipeng Xu

Abstract

We give three explicit quantum Latin squares of order $6$ , with cardinalities $13$ , $15$ , and $17$ . Throughout, vectors differing only by a global phase are counted as identical. The cardinality- $13$ construction is based on an orthogonal direct-sum decomposition $\C^6=\C^4\oplus\C^2$ . The cardinality- $15$ and cardinality- $17$ constructions are based on two-dimensional Hadamard pairs supported on coordinate planes.

Keywords

quantum Latin squares order 6 cardinality Hadamard pairs orthogonal decomposition complex vector space global phase

Cite

@article{arxiv.2605.15540,
  title  = {Three Quantum Latin Squares of Order 6 with Cardinalities 13, 15, and 17},
  author = {Zhipeng Xu},
  journal= {arXiv preprint arXiv:2605.15540},
  year   = {2026}
}

Three Quantum Latin Squares of Order 6 with Cardinalities 13, 15, and 17

Abstract

Keywords

Cite

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