Related papers: Orthogonality for Quantum Latin Isometry Squares
We investigate sets of Mutually Orthogonal Latin Squares (MOLS) generated by Cellular Automata (CA) over finite fields. After introducing how a CA defined by a bipermutive local rule of diameter $d$ over an alphabet of $q$ elements…
In this paper we propose an algorithm for enumerating diagonal Latin squares of small order. It relies on specific properties of diagonal Latin squares to employ symmetry breaking techniques, and on several heuristic optimizations and bit…
Difference arrays are used in applications such as software testing, authentication codes and data compression. Pseudo-orthogonal Latin squares are used in experimental designs. A special class of pseudo-orthogonal Latin squares are the…
We introduce a new graphical framework for designing quantum error correction codes based on classical principles. A key feature of this graphical language, over previous approaches, is that it is closely related to that of factor graphs or…
Symmetries of a partial Latin square are determined by its autotopism group. Analogously to the case of Latin squares, given an isotopism $\Theta$, the cardinality of the set $\mathcal{PLS}_{\Theta}$ of partial Latin squares which are…
We recall the Alon-Tarsi conjecture on the number of even latin squares. We introduce a map which switches the parity of a latin square under certain requirements. An example is included.
A unified approach, for solving a wide class of single and many-body quantum problems, commonly encountered in literature is developed based on a recently proposed method for finding solutions of linear differential equations. Apart from…
We develop a new method for constructing "good" designs for computer experiments. The method derives its power from its basic structure that builds large designs using small designs. We specialize the method for the construction of…
Latin squares have been historically used in order to create statistical designs in which, starting from a small number of experiments, it can be obtained a large experimental space. In this sense, the optimization of the selection of Latin…
We introduce a graph attached to mutually orthogonal Sudoku Latin squares. The spectra of the graphs obtained from finite fields are explicitly determined. As a corollary, we then use the eigenvalues to distinguish non-isomorphic Sudoku…
We show that any partial Latin square of order $n$ can be embedded in a Latin square of order at most $16n^2$ which has at least $2n$ mutually orthogonal mates. We also show that for any $t\geq 2$, a pair of orthogonal partial Latin squares…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
In this paper, we explore the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds for scalable, fault-tolerant quantum computation. To circumvent the traditionally low thresholds of small…
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…
I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum…
An exploratory approach to the possibility of analyzing nonorthogonality as a quantifiable property is presented. Three different measures for the nonorthogonality of pure states are introduced, and one of these measures is extended to…
A Latin square of order $n$ is an $n \times n$ matrix of $n$ symbols, such that each symbol occurs exactly once in each row and column. For an odd prime power $q$ let $\mathbb{F}_q$ denote the finite field of order $q$. A quadratic Latin…
We introduce the notion of noncommutative complex spheres with partial commutation relations for the coordinates. We compute the corresponding quantum symmetry groups of these spheres, and this yields new quantum unitary groups with partial…
We introduce a notion of parity for transversals, and use it to show that in Latin squares of order $2 \bmod 4$, the number of transversals is a multiple of 4. We also demonstrate a number of relationships (mostly congruences modulo 4)…
Commonly the direct construction and the description of mutually orthogonal Latin squares (MOLS) makes use of difference or quasi-difference matrices. Now there exists a correspondence between MOLS and separable permutation codes. We like…