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In the first part of this work, we show how certain techniques from quantum information theory can be used in order to obtain very sharp embeddings between noncommutative Lp-spaces. Then, we use these estimates to study the classical capacity wi[...]texto impreso
In this paper we show how the metric theory of tensor products developed by Grothendieck perfectly fits in the study of channel capacities, a central topic in Shannon’s information theory. Furthermore, in the last years Shannon’s theory has been[...]texto impreso
Navascués Cobo, Miguel ; Pérez García, David ; Junge, Marius ; Palazuelos Cabezón, Carlos ; Scholz, V. B. ; R. F. Werner, R. F. | American Institute of Physics | 2011We show that Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg's QWEP conjecture) are essentially equivalent. Specif[...]texto impreso
González Guillén, Carlos Eduardo ; Palazuelos Cabezón, Carlos ; Villanueva, Ignacio | Springer New York LLC | 2016In this work, we study a version of the general question of how well a Haar-distributed orthogonal matrix can be approximated by a random Gaussian matrix. Here, we consider a Gaussian random matrix (Formula presented.) of order n and apply to it[...]texto impreso
Palazuelos Cabezón, Carlos ; Peralta Pereira, Antonio Miguel ; Villanueva, Ignacio | Polish Acad Sciencies Inst Mathematics | 2009In recent papers, the Right mid the Strong* topologies have been. introduced and studied on general Banach spaces We characterize different types of continuity for multilinear operators (joint, uniform, etc) with respect to the above topologies [...]texto impreso
Jarchow , Hans ; Palazuelos Cabezón, Carlos ; Pérez García, David ; Villanueva, Ignacio | Academic Press | 2007-12-15The aim of this paper is to investigate close relations between the validity of Hahn–Banach extension theorems for multilinear forms on Banach spaces and summability properties of sequences from these spaces. A case of particular importance occu[...]texto impreso
Junge, M. ; Palazuelos Cabezón, Carlos ; Parcet, J. ; Perrin, M. | American Institute of Physics | 2015-02We obtain hypercontractivity estimates for a large class of semigroups defined on finite-dimensional matrix algebras Mn. These semigroups arise from Poisson-like length functions ? on Zn × Zn and provide new hypercontractive families of quantum [...]texto impreso
In this paper we introduce a simple and natural bipartite Bell scenario, by considering the correlations between two parties defined by general measurements in one party and dichotomic ones in the other. We show that unbounded Bell violations ca[...]texto impreso
In this paper we obtain violations of general bipartite Bell inequalities of order root n/log n with n inputs, n outputs and n-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involv[...]texto impreso
Palazuelos Cabezón, Carlos ; Sánchez Pérez, Enrique A. ; Tradacete Pérez, Pedro | The Theta Foundation | 2012We characterize by means of a vector norm inequality the space of operators that factorize through a p-summing operator from an L-r-space to an L-s-space. As an application, we prove a domination result in the sense of Dodds-Fremlin for p-summin[...]texto impreso
We study the projective tensor norm as a measure of the largest Bell violation of a quantum state. In order to do this, we consider a truncated version of a well-known SDP relaxation for the quantum value of a two-prover one-round game, one whic[...]texto impreso
Junge, M. ; Pérez García, David ; Palazuelos Cabezón, Carlos ; Villanueva, Ignacio ; Wolf, Michael | American Physical Society | 2009In this letter we show that the field of Operator Space Theory provides a general and powerful mathematical framework for arbitrary Bell inequalities, in particular regarding the scaling of their violation within quantum mechanics. We illustrate[...]texto impreso
Villanueva, Ignacio ; Palazuelos Cabezón, Carlos ; Peralta Pereira, Antonio Miguel | Oxford University Press | 2008-09We show that for every orthogonally additive scalar n-homogeneous polynomial P on a C*-algebra A there exists phi in A* satisfying P(x) = phi(x(n)), for each element x in A. The vector-valued analogue follows as a corollary.texto impreso
González-Guillén, Carlos E. ; Lancien, Cécilia ; Palazuelos Cabezón, Carlos ; Villanueva, Ignacio | Springer | 2017It is now a well-known fact that the correlations arising from local dichotomic measurements on an entangled quantum state may exhibit intrinsically non-classical features. In this paper we delve into a comprehensive study of random instances of[...]texto impreso
In this work, we study rank-one quantum games. In particular, we focus on the study of the computability of the entangled value ?*. We show that the value ?* can be efficiently approximated up to a multiplicative factor of 4. We also study the b[...]
