5 papers
Enumeration of Laplacian integral and {-1,0,1}-diagonalizable graphs
Nathaniel Johnston, Sarah Plosker, Luis M. B. Varona
A graph with Laplacian matrix is called Laplacian integral if the eigenvalues of are all integers, and it is called -diagonalizable if has a full set of eig…
Graph Structures for Local Distinguishability of Quantum Product States
Sooyeong Kim, David W. Kribs, Michael Nathanson +2
We consider the problem of distinguishing sets of quantum product states with local operations and classical communication (LOCC). Recent work has used graph theory to identify set…
Generalizing the Cauchy-Schwarz inequality: Hadamard powers and tensor products
Nathaniel Johnston, Sarah Plosker, Charles Torrance +1
We explore and generalize a Cauchy-Schwarz-type inequality originally proved in [Electronic Journal of Linear Algebra 35, 156-180 (2019)]: $\|\mathbf{v}^2\|\|\mathbf{w}^2\| - \lang…
The Factor Width Rank of a Matrix
Nathaniel Johnston, Shirin Moein, Sarah Plosker
A matrix is said to have factor width at most if it can be written as a sum of positive semidefinite matrices that are non-zero only in a single principal submatri…
Laplacian - and -diagonalizable graphs
Nathaniel Johnston, Sarah Plosker
A graph is called "Laplacian integral" if the eigenvalues of its Laplacian matrix are all integers. We investigate the subset of these graphs whose Laplacian is furthermore diagona…