A weak Hadamard matrix is a $\{-1,0, 1\}$-matrix $P$ such that $PP^T$ is tridiagonal. We explore the underlying algebraic and combinatorial structure of weak Hadamard matrices and weakly Hadamard diagonalizable graphs (graphs whose Laplacian matrix is diagonalized by a weak Hadamard matrix). We also provide constructions and examples of such matrices and graphs. We then consider quantum state transfer with respect to such graphs.Comment: 26 pages, 1 figure, 1 tabl
We explore algebraic and spectral properties of weighted graphs containing twin vertices that are us...
An Hadamard matrix H is a matrix of order n all of whose elements are + 1 or -1 and which satisfies ...
Abstract. Applications in quantum information theory and quantum tomography have raised current inte...
Quantum state transfer within a quantum computer can be achieved by using a network of qubits, and s...
If the Laplacian matrix of a graph has a full set of orthogonal eigenvectors with entries ±1, then t...
AbstractOf interest here is a characterization of the undirected graphs G such that the Laplacian ma...
An Hadamard matrix is a square matrix $H\in M_N(\pm1)$ whose rows and pairwise orthogonal. Such matr...
AbstractOf interest here is a characterization of the undirected graphs G such that the Laplacian ma...
A computer has been used to list all known Hadamard matrices of order less than 40,000. If an Hadama...
Hadamard matrices have been studied by many authors, but higher-dimensional generalizations of Hadam...
Let $n$ be the order of a (quaternary) Hadamard matrix. It is shown that the existence of a projecti...
Given any natural number q \u3e 3 we show there exists an integer t ≤ [2 log2 (q – 3)] such that an ...
AbstractGiven any natural number q > 3 we show there exists an integer t ⩽ [2log2(q − 3)] such that ...
A Hadamard matrix is balanced splittable if some subset of its rows has the property that the dot pr...
© 2015 AIP Publishing LLC. Graph states are widely used in quantum information theory, including ent...
We explore algebraic and spectral properties of weighted graphs containing twin vertices that are us...
An Hadamard matrix H is a matrix of order n all of whose elements are + 1 or -1 and which satisfies ...
Abstract. Applications in quantum information theory and quantum tomography have raised current inte...
Quantum state transfer within a quantum computer can be achieved by using a network of qubits, and s...
If the Laplacian matrix of a graph has a full set of orthogonal eigenvectors with entries ±1, then t...
AbstractOf interest here is a characterization of the undirected graphs G such that the Laplacian ma...
An Hadamard matrix is a square matrix $H\in M_N(\pm1)$ whose rows and pairwise orthogonal. Such matr...
AbstractOf interest here is a characterization of the undirected graphs G such that the Laplacian ma...
A computer has been used to list all known Hadamard matrices of order less than 40,000. If an Hadama...
Hadamard matrices have been studied by many authors, but higher-dimensional generalizations of Hadam...
Let $n$ be the order of a (quaternary) Hadamard matrix. It is shown that the existence of a projecti...
Given any natural number q \u3e 3 we show there exists an integer t ≤ [2 log2 (q – 3)] such that an ...
AbstractGiven any natural number q > 3 we show there exists an integer t ⩽ [2log2(q − 3)] such that ...
A Hadamard matrix is balanced splittable if some subset of its rows has the property that the dot pr...
© 2015 AIP Publishing LLC. Graph states are widely used in quantum information theory, including ent...
We explore algebraic and spectral properties of weighted graphs containing twin vertices that are us...
An Hadamard matrix H is a matrix of order n all of whose elements are + 1 or -1 and which satisfies ...
Abstract. Applications in quantum information theory and quantum tomography have raised current inte...
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