34 citations · 207 across the 35 of their papers we have counts for
41 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…
Weakly Hadamard diagonalizable graphs and Quantum State Transfer
Darian McLaren, Hermie Monterde, Sarah Plosker
Hadamard diagonalizable graphs are undirected graphs for which the corresponding Laplacian is diagonalizable by a Hadamard matrix. Such graphs have been studied in the context of q…
Absolutely -Incoherent Quantum States and Spectral Inequalities for Factor Width of a Matrix
Nathaniel Johnston, Shirin Moein, Rajesh Pereira +1
We investigate the set of quantum states that can be shown to be -incoherent based only on their eigenvalues (equivalently, we explore which Hermitian matrices can be shown to h…
Quantum state transfer between twins in weighted graphs
Stephen Kirkland, Hermie Monterde, Sarah Plosker
Twin vertices in simple unweighted graphs are vertices that have the same neighbours and, in the case of weighted graphs with possible loops, the corresponding incident edges have…
Birkhoff-James Orthogonality in the Trace Norm, with Applications to Quantum Resource Theories
Nathaniel Johnston, Shirin Moein, Rajesh Pereira +1
We develop numerous results that characterize when a complex Hermitian matrix is Birkhoff-James orthogonal, in the trace norm, to a (Hermitian) positive semidefinite matrix or set…
Expanding Cybersecurity Knowledge Through an Indigenous Lens: A First Look
Farrah Huntinghawk, Candace Richard, Sarah Plosker +1
Decolonization and Indigenous education are at the forefront of Canadian content currently in Academia. Over the last few decades, we have seen some major changes in the way in whi…
Universality of Weyl Unitaries
Douglas Farenick, Oluwatobi Ruth Ojo, Sarah Plosker
Weyl's unitary matrices, which were introduced in Weyl's 1927 paper on group theory and quantum mechanics, are unitary matrices given by the diagonal matrix whose entri…
The Complete Positivity of Symmetric Tridiagonal and Pentadiagonal Matrices
Lei Cao, Darian McLaren, Sarah Plosker
We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix is completely positive. Our decomposition can be applied to a wide range of matrice…
Complete Order Equivalence of Spin Unitaries
Douglas Farenick, Farrah Huntinghawk, Adili Masanika +1
This paper is a study of linear spaces of matrices and linear maps on matrix algebras that arise from \emph{spin systems}, or \emph{spin unitaries}, which are finite sets $\mathcal…
Bistochastic operators and quantum random variables
Sarah Plosker, Christopher Ramsey
Given a positive operator-valued measure acting on the Borel sets of a locally compact Hausdorff space , with outcomes in the algebra of all bounded…
Complex Hadamard Diagonalisable Graphs
Ada Chan, Shaun Fallat, Steve Kirkland +3
In light of recent interest in Hadamard diagonalisable graphs (graphs whose Laplacian matrix is diagonalisable by a Hadamard matrix), we generalise this notion from real to complex…
Centrosymmetric Stochastic Matrices
Lei Cao, Darian McLaren, Sarah Plosker
We consider the convex set of stochastic matrices and the convex set of centrosymmetric stochastic matrices (stochastic…
Quantum Majorization on Semifinite von Neumann Algebras
Priyanga Ganesan, Li Gao, Satish K. Pandey +1
We extend Gour et al's characterization of quantum majorization via conditional min-entropy to the context of semifinite von Neumann algebras. Our method relies on a connection bet…
Achievable multiplicity partitions in the inverse eigenvalue problem of a graph
Mohammad Adm, Shaun Fallat, Karen Meagher +3
Associated to a graph is a set of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the gr…
Approximately Clean Quantum Probability Measures
Douglas Farenick, Remus Floricel, Sarah Plosker
A quantum probability measure--or quantum measurement--is said to be clean if it cannot be irreversibly connected to any other quantum probability measure via a quantum channel. Th…
Schur multipliers and mixed unitary maps
Samuel J. Harris, Rupert H. Levene, Vern I. Paulsen +2
We consider the tensor product of the completely depolarising channel on matrices with the map of Schur multiplication by a correlation matrix and characte…
A simplified and unified generalization of some majorization results
Shirin Moein, Rajesh Pereira, Sarah Plosker
We consider positive, integral-preserving linear operators acting on space, known as stochastic operators or Markov operators. We show that, on finite-dimensional spaces, any…
Some notes on the robustness of k-coherence and k-entanglement
Nathaniel Johnston, Chi-Kwong Li, Sarah Plosker +2
We show that two related measures of k-coherence, called the standard and generalized robustness of k-coherence, are equal to each other when restricted to pure states. As a direct…
Switching and partially switching the hypercube while maintaining perfect state transfer
Steve Kirkland, Sarah Plosker, Xiaohong Zhang
A graph is said to exhibit perfect state transfer (PST) if one of its corresponding Hamiltonian matrices, which are based on the vertex-edge structure of the graph, gives rise to P…
An operator-valued Lyapunov theorem
Sarah Plosker, Christopher Ramsey
We generalize Lyapunov's convexity theorem for classical (scalar-valued) measures to quantum (operator-valued) measures. In particular, we show that the range of a nonatomic quantu…