Roy Araiza
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View article: Transportation cost and contraction coefficient for channels on von Neumann algebras
Transportation cost and contraction coefficient for channels on von Neumann algebras Open
We present a noncommutative optimal transport framework for quantum channels acting on von Neumann algebras. Our central object is the Lipschitz cost measure, a transportation-inspired quantity that evaluates the minimal cost required to m…
View article: On a question of Blecher, Pisier, Shlyakhtenko
On a question of Blecher, Pisier, Shlyakhtenko Open
We show the failure of a matricial version of Grothendieck's theorem for operator spaces, thereby resolving a long-standing open question in the field. Moreover, by showing that such a counterexample can occur in the simplest context of co…
View article: A note on the stabilizer formalism via noncommutative graphs
A note on the stabilizer formalism via noncommutative graphs Open
In this short note we formulate a stabilizer formalism in the language of noncommutative graphs. The classes of noncommutative graphs we consider are obtained via unitary representations of compact groups, and suitably chosen operators on …
View article: Resource-Dependent Complexity of Quantum Channels
Resource-Dependent Complexity of Quantum Channels Open
We introduce a new framework for quantifying the complexity of quantum channels, grounded in a suitably chosen resource set. This class of convex functions is designed to analyze the complexity of both open and closed quantum systems. By l…
View article: Operator Systems Generated by Projections
Operator Systems Generated by Projections Open
We construct a family of operator systems and $k$-AOU spaces generated by a finite number of projections satisfying a set of linear relations. This family is universal in the sense that the map sending the generating projections to any oth…
View article: An Index for Inclusions of Operator Systems
An Index for Inclusions of Operator Systems Open
Inspired by a well-known characterization of the index of an inclusion of II$_1$ factors due to Pimsner and Popa, we define an index-type invariant for inclusions of operator systems. We compute examples of this invariant, show that it is …
View article: Approximating projections by quantum operations
Approximating projections by quantum operations Open
Using techniques from semidefinite programming, we study the problem of finding a closest quantum channel to the projection onto a matricial subsystem. We derive two invariants of matricial subsystems which are related to the quantum Lovás…
View article: Matricial Archimedean order unit spaces and quantum correlations
Matricial Archimedean order unit spaces and quantum correlations Open
We introduce a matricial analogue of an Archimedean order unit space, which we call a $k$-AOU space. We develop the category of $k$-AOU spaces and $k$-positive maps and exhibit functors from this category to the category of operator system…
View article: An abstract characterization for projections in operator systems
An abstract characterization for projections in operator systems Open
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 $p$ is a positive contraction in an operator system $V$ which satisfies certain or…