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Quantum Latin squares with all possible cardinalities
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Quantum Latin squares with all possible cardinalities
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A quantum Latin square of order $n$ (denoted as QLS$(n)$) is an $n\times n$ 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 $|u\rangle, |v\rangle\in \mathcal{H}_n$ are regarded as identical if there exists a real number $\theta$ such that $|u\rangle=e^{i\theta}|v\rangle$; otherwise, they are considered distinct. The cardinality $c$ of a QLS$(n)$ is the number of distinct vectors in the array. In this paper, we use sub-QLS$(4)$s to prove that for any integer $m\geq 2$ and any integer $c\in [4m,16m^2]\setminus \{4m+1\}$, there is a QLS$(4m)$ with cardinality $c$.
Forward citations
Cited by 4 Pith papers
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New Cardinalities for Quantum Latin Squares of Order Six
Explicit order-6 quantum Latin squares exist with cardinalities 19, 21, and 23, completing all values in 6–24 except the impossible 7.
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New Cardinalities for Quantum Latin Squares of Order Six
Explicit six-by-six quantum Latin squares with 19, 21, 23, 25, and 27 distinct states are constructed, completing the order-six cardinality list through 28.
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Three Quantum Latin Squares of Order 6 with Cardinalities 13, 15, and 17
Two explicit quantum Latin squares of order 6 are constructed with cardinalities 13 and 17 using direct-sum decompositions and Hadamard pairs.
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Three Quantum Latin Squares of Order 6 with Cardinalities 13, 15, and 17
Explicit constructions of three quantum Latin squares of order 6 achieving cardinalities 13, 15, and 17 via orthogonal decompositions and Hadamard pairs.
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