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Quantum State Preparation Representation

Quantum Latin squares of order 6m with all possible cardinalities

arXiv
Authors: Ying Zhang, Lijun Ji

Year

2026

Paper ID

3855

Status

Preprint

Abstract Read

~2 min

Abstract Words

122

Citations

N/A

Abstract

A quantum Latin square of order n (denoted as QLS(n)) is an ntimes n array whose entries are unit column vectors from the n-dimensional Hilbert space mathcal{H}n, such that each row and column forms an orthonormal basis. Two unit vectors |urangle, |vranglein mathcal{H}n are regarded as identical if there exists a real number θ such that |urangle=eiθ|vrangle; otherwise, they are considered distinct. The cardinality c of a QLS(n) is the number of distinct vectors in the array. In this note,we use sub-QLS(6) to prove that for any integer mgeq 2 and any cin \[6m,36m2\]setminus \{6m+1\}, there is a QLS(6m) with cardinality c.

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  • A quantum Latin square of order n (denoted as QLS(n)) is an ntimes n array whose entries are unit column vectors from the n-dimensional Hilbert space mathcalHn, such that each...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2601.09132 [2] arXiv https://arxiv.org/abs/2601.09132 [3] Publisher https://arxiv.org/abs/2601.09132

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