8 citations · 29 across the 17 of their papers we have counts for
19 papers
On C*-nuclearity of graph operator systems
Adam Dor-On, Travis Russell
We classify the set of finite simple undirected graphs whose corresponding graph operator system is C*-nuclear. We prove that the operator system associated to the graph is C*-nucl…
-extreme maps and -homomorphisms from to finite von Neumann algebras
Dimitrios Giannakis, Michael Montgomery, Travis Russell
Given a unital inclusion of -algebras and a unital inclusion into a von Neumann algebra , we invest…
Approximate factorization properties for operator systems
Roy Araiza, Larissa Kroell, Travis Russell +1
We show that many of the standard nuclearity properties considered in the literature for the hierarchy of operator system tensor products can be expressed as approximate factorizat…
Products and factorization in operator systems
Adam Dor-On, Travis B. Russell
We study unital operator spaces endowed with a partially defined product. We give a matrix-norm characterization of such products that allows for a representation theorem where the…
Real operator systems
David P. Blecher, Travis B. Russell
Operator systems are the unital self-adjoint subspaces of the bounded operators on a Hilbert space. Complex operator systems are an important category containing the C*-algebras an…
Operator system characterizations of SIC-POVMs and mutually unbiased bases
Travis B. Russell
We show that a symmetric informationally-complete positive operator-valued measure exists in a given dimension if and only if there exists a -dimensional operator system s…
Operator Systems Generated by Projections
Roy Araiza, Travis Russell
We construct a family of operator systems and -AOU spaces generated by a finite number of projections satisfying a set of linear relations. This family is universal in the sense…
Synchronous Values of Games
J. William Helton, Hamoon Mousavi, Seyed Sajjad Nezhadi +2
We study synchronous values of games, especially synchronous games. It is known that a synchronous game has a perfect strategy if and only if it has a perfect synchronous strategy.…
Matricial Archimedean order unit spaces and quantum correlations
Roy Araiza, Travis Russell, Mark Tomforde
We introduce a matricial analogue of an Archimedean order unit space, which we call a -AOU space. We develop the category of -AOU spaces and -positive maps and exhibit fun…
A synchronous NPA hierarchy with applications
Travis B. Russell
We present an adaptation of the NPA hierarchy to the setting of synchronous correlation matrices. Our adaptation improves upon the original NPA hierarchy by using smaller certifica…
A Universal Representation for Quantum Commuting Correlations
Roy Araiza, Travis Russell, Mark Tomforde
We explicitly construct an Archimedean order unit space whose state space is affinely isomorphic to the set of quantum commuting correlations. Our construction only requires fundam…
Maximally entangled correlation sets
Elie Alhajjar, Travis Russell
We study the set of quantum correlations generated by actions on maximally entangled states. We show that such correlations are dense in their own convex hull. As a consequence, we…
An abstract characterization for projections in operator systems
Roy Araiza, Travis Russell
We show that the set of projections in an operator system can be detected using only the abstract data of the operator system. Specifically, we show that if is a positive contr…
No quantum Ramsey theorem for stabilizer codes
Yannis Bousba, Travis B. Russell
In this paper we study the quantum graphs of mixed-unitary channels generated by tensor products of Pauli operators, which we call Pauli channels. We show that most quantum graphs…
Two-outcome synchronous correlation sets and Connes' embedding problem
Travis B. Russell
We show that Connes' embedding problem is equivalent to the weak Tsirelson problem in the setting of two-outcome synchronous correlation sets. We further show that the extreme poin…
Geometry of the set of synchronous quantum correlations
Travis B. Russell
We provide a complete geometric description of the set of synchronous quantum correlations for the three experiment two outcome scenario. We show that these correlations form a clo…
Characterizations of ordered operator spaces
Travis B. Russell
We demonstrate new abstract characterizations for unital and non-unital operator spaces. We characterize unital operator spaces in terms of the cone of accretive operators (operato…
Characterizations of Ordered Self-adjoint Operator Spaces
Travis B. Russell
We describe how self-adjoint ordered operator spaces, also called non-unital operator systems in the literature, can be understood as -vector spaces equipped with a matrix gauge…
The exact synthesis of 1- and 2-qubit Clifford+T circuits
Travis Russell
We describe a new method for the decomposition of an arbitrary qubit operator with entries in , i.e., of the form $(a+b\sqrt{2}+i(c+d\sqrt{2})…