REVIEW 5 cited by
On the cardinalities of quantum Latin squares
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
On the cardinalities of quantum Latin squares
read the original abstract
A quantum Latin square of order $v$, QLS($v$), is a $v\times v$ array in which each of entries is a unit column vector from the Hilbert space $\mathbb{C}^{v}$, such that every row and column forms an orthonormal basis of $\mathbb{C}^{v}$. The cardinality of a QLS($v$) is the number of its vectors distinct up to a global phase, which is the crucial indicator for distinguishing between classical QLSs and non-classical QLSs. In this paper, we investigate the possible cardinalities of a QLS($v$). As a result, we completely resolve the existence of a QLS($v$) with maximal cardinality for any $v\geq 4$. Moreover, based on Wilson's construction and Direct Product construction, we establish some possible cardinality range of a QLS($v$) for any $v\geq 4$.
Forward citations
Cited by 5 Pith papers
-
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.
-
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.
-
The Existence of Diagonal Quantum Latin Squares with Maximum Cardinality
MCDQLS(n) exists for all but a few n, based on constructions for idempotent MCQLS(n) and implying results for MCPQLS(n).
-
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.
-
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.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.