Rupert H. Levene
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Rupert H. Levene has a total of 40 co-authors. Here are the top co-authors by number of shared publications:
- Ivan G. Todorov
School of Mathematical Sciences University of Delaware Newark, DE 19716, USA
10 shared publications - David W. Kribs
University of Guelph
6 shared publications - Helena Šmigoc
School of Mathematics and Statistics University College Dublin Belfield Dublin 4 Ireland
6 shared publications - Jason Crann
School of Mathematics and Statistics, Carleton University, Ottawa, Canada
5 shared publications - Polona Oblak
Faculty of Computer and Information Science, University of Ljubljana, Ljubljana, Slovenia
5 shared publications - Lyudmila Turowska
Department of Mathematical Sciences Chalmers University of Technology
4 shared publications
Latest Publications
- Open Access
- 1 January 2026
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 67 (1)
Unique games and games based on groups
We study unique games and estimate some of their values. We prove that if a unique game has a quantum-assisted value close to 1, then it must have a perfect deterministic strategy. We introduce a family of unique games based on groups that generalize XOR games, and show that when the group is the cyclic group of order 3, then these games correspond to a 3-labelling problem for directed graphs.
- 1 January 2026
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 67 (1)
Open AccessUnique games and games based on groups
We study unique games and estimate some of their values. We prove that if a unique game has a quantum-assisted value close to 1, then it must have a perfect deterministic strategy. We introduce a family of unique games based on groups that generalize XOR games, and show that when the group is the cyclic group of order 3, then these games correspond to a 3-labelling problem for directed graphs.
- Open Access
Unique Games and Games Based on Groups
We study unique games and estimate some of their values. We prove that if a unique game has a quantum-assisted value close to 1, then it must have a perfect deterministic strategy. We introduce a family of unique games based on groups that generalize XOR games, and show that when the group is the cyclic group of order 3, then these games correspond to a 3-labelling problem for directed graphs.
Open AccessUnique Games and Games Based on Groups
We study unique games and estimate some of their values. We prove that if a unique game has a quantum-assisted value close to 1, then it must have a perfect deterministic strategy. We introduce a family of unique games based on groups that generalize XOR games, and show that when the group is the cyclic group of order 3, then these games correspond to a 3-labelling problem for directed graphs.
- 14 July 2024
- Published by Elsevier in Journal of Combinatorial Theory, Series B
- Vol. 169, 161-210
Spectral arbitrariness for trees fails spectacularly
- 14 July 2024
- Published by Elsevier in Journal of Combinatorial Theory, Series B
- Vol. 169, 161-210
Spectral arbitrariness for trees fails spectacularly
- Open Access
Values of cooperative quantum games
We develop a resource-theoretical approach that allows us to quantify values of two-player, one-round cooperative games with quantum inputs and outputs, as well as values of quantum probabilistic hypergraphs. We analyse the quantum game values arising from the type hierarchy of quantum no-signalling correlations, establishing tensor norm expressions for each of the correlation types. As a consequence, we provide metric characterisations of state convertibility via LOSR and LOCC.En route, we obtain an alternative description of the maximal tensor products of ternary rings of operators.
Open AccessValues of cooperative quantum games
We develop a resource-theoretical approach that allows us to quantify values of two-player, one-round cooperative games with quantum inputs and outputs, as well as values of quantum probabilistic hypergraphs. We analyse the quantum game values arising from the type hierarchy of quantum no-signalling correlations, establishing tensor norm expressions for each of the correlation types. As a consequence, we provide metric characterisations of state convertibility via LOSR and LOCC.En route, we obtain an alternative description of the maximal tensor products of ternary rings of operators.
- Open Access
Bordering of Symmetric Matrices and an Application to the Minimum Number of Distinct Eigenvalues for the Join of Graphs
An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the join of a connected graph with a path. We then focus on bordering a matrix and attempt to control the change in the number of distinct eigenvalues induced by this operation. By applying bordering techniques to the join of graphs, we obtain numerous results on the nature of the minimum number of distinct eigenvalues as vertices are joined to a fixed graph.
Open AccessBordering of Symmetric Matrices and an Application to the Minimum Number of Distinct Eigenvalues for the Join of Graphs
An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the join of a connected graph with a path. We then focus on bordering a matrix and attempt to control the change in the number of distinct eigenvalues induced by this operation. By applying bordering techniques to the join of graphs, we obtain numerous results on the nature of the minimum number of distinct eigenvalues as vertices are joined to a fixed graph.
- Open Access
- 10 July 2023
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 72 (12) , 2054-2068
Distinct eigenvalues are realizable with generic eigenvectors
- 10 July 2023
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 72 (12) , 2054-2068
Open AccessDistinct eigenvalues are realizable with generic eigenvectors
- Open Access
Spectral arbitrariness for trees fails spectacularly
If $G$ is a graph and $\mathbf{m}$ is an ordered multiplicity list which is realizable by at least one symmetric matrix with graph $G$, what can we say about the eigenvalues of all such realizing matrices for $\mathbf{m}$? It has sometimes been tempting to expect, especially in the case that $G$ is a tree, that any spacing of the multiple eigenvalues should be realizable. In 2004, however, F. Barioli and S. Fallat produced the first counterexample: a tree on 16 vertices and an ordered multiplicity list for which every realizing set of eigenvalues obeys a nontrivial linear constraint. We extend this by giving an infinite family of trees and ordered multiplicity lists whose sets of realizing eigenvalues are very highly constrained, with at most 5 degrees of freedom, regardless of the size of the tree in this family. In particular, we give the first examples of multiplicity lists for a tree which impose nontrivial nonlinear eigenvalue constraints and produce an ordered multiplicity list which is achieved by a unique set of eigenvalues, up to shifting and scaling.Open AccessSpectral arbitrariness for trees fails spectacularly
If $G$ is a graph and $\mathbf{m}$ is an ordered multiplicity list which is realizable by at least one symmetric matrix with graph $G$, what can we say about the eigenvalues of all such realizing matrices for $\mathbf{m}$? It has sometimes been tempting to expect, especially in the case that $G$ is a tree, that any spacing of the multiple eigenvalues should be realizable. In 2004, however, F. Barioli and S. Fallat produced the first counterexample: a tree on 16 vertices and an ordered multiplicity list for which every realizing set of eigenvalues obeys a nontrivial linear constraint. We extend this by giving an infinite family of trees and ordered multiplicity lists whose sets of realizing eigenvalues are very highly constrained, with at most 5 degrees of freedom, regardless of the size of the tree in this family. In particular, we give the first examples of multiplicity lists for a tree which impose nontrivial nonlinear eigenvalue constraints and produce an ordered multiplicity list which is achieved by a unique set of eigenvalues, up to shifting and scaling. - 23 December 2022
- Published by Springer Nature in Annales Henri Poincare
- Vol. 24 (5) , 1779-1821
Quantum Teleportation in the Commuting Operator Framework
- 23 December 2022
- Published by Springer Nature in Annales Henri Poincare
- Vol. 24 (5) , 1779-1821
Quantum Teleportation in the Commuting Operator Framework
- Open Access
Quantum teleportation in the commuting operator framework
We introduce a notion of teleportation scheme between subalgebras of semi-finite von Neumann algebras in the commuting operator model of locality. Using techniques from subfactor theory, we present unbiased teleportation schemes for relative commutants $N'\cap M$ of a large class of finite-index inclusions $N\subseteq M$ of tracial von Neumann algebras, where the unbiased condition means that no information about the teleported observables are contained in the classical communication sent between the parties. For a large class of subalgebras $N$ of matrix algebras $M_n(\mathbb{C})$, including those relevant to hybrid classical/quantum codes, we show that any tight teleportation scheme for $N$ necessarily arises from an orthonormal unitary Pimsner-Popa basis of $M_n(\mathbb{C})$ over $N'$, generalising work of Werner. Combining our techniques with those of Brannan-Ganesan-Harris, we compute quantum chromatic numbers for a variety of quantum graphs arising from finite-dimensional inclusions $N\subseteq M$.Open AccessQuantum teleportation in the commuting operator framework
We introduce a notion of teleportation scheme between subalgebras of semi-finite von Neumann algebras in the commuting operator model of locality. Using techniques from subfactor theory, we present unbiased teleportation schemes for relative commutants $N'\cap M$ of a large class of finite-index inclusions $N\subseteq M$ of tracial von Neumann algebras, where the unbiased condition means that no information about the teleported observables are contained in the classical communication sent between the parties. For a large class of subalgebras $N$ of matrix algebras $M_n(\mathbb{C})$, including those relevant to hybrid classical/quantum codes, we show that any tight teleportation scheme for $N$ necessarily arises from an orthonormal unitary Pimsner-Popa basis of $M_n(\mathbb{C})$ over $N'$, generalising work of Werner. Combining our techniques with those of Brannan-Ganesan-Harris, we compute quantum chromatic numbers for a variety of quantum graphs arising from finite-dimensional inclusions $N\subseteq M$. - Open Access
- 1 August 2022
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 652, 213-238
Orthogonal symmetric matrices and joins of graphs
- 1 August 2022
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 652, 213-238
Open AccessOrthogonal symmetric matrices and joins of graphs