Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Araiza, Roy"'
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 commutative $
Externí odkaz:
http://arxiv.org/abs/2406.05302
Autor:
Araiza, Roy, Cai, Jihong, Chen, Yushan, Holtermann, Abraham, Hsu, Chieh, Mohan, Tushar, Wu, Peixue, Yu, Zeyuan
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 finite-dime
Externí odkaz:
http://arxiv.org/abs/2310.00762
Quantum complexity theory is concerned with the amount of elementary quantum resources needed to build a quantum system or a quantum operation. The fundamental question in quantum complexity is to define and quantify suitable complexity measures. Thi
Externí odkaz:
http://arxiv.org/abs/2303.11304
Autor:
Araiza, Roy, Russell, Travis
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 other set of p
Externí odkaz:
http://arxiv.org/abs/2302.12951
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 multiplicat
Externí odkaz:
http://arxiv.org/abs/2203.05710
Publikováno v:
Linear Algebra Appl. 663 (2023), 178-199
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 Lov\'asz theta f
Externí odkaz:
http://arxiv.org/abs/2203.02627
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 systems and compl
Externí odkaz:
http://arxiv.org/abs/2109.11671
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 fundamental techniques from the theory of order unit spaces and operator sys
Externí odkaz:
http://arxiv.org/abs/2102.05827
Autor:
Araiza, Roy, Russell, Travis
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 order-theoret
Externí odkaz:
http://arxiv.org/abs/2006.03094
Publikováno v:
In Linear Algebra and Its Applications 15 April 2023 663:178-199
