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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
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 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
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
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[...]texto impreso
We show how a vector-valued version of Schechtmans empirical method can be used to reduce the number of questions in a nonlocal game G while preserving the quotient ?*(G)/?(G) of the quantum over the classical bias. We apply our method to the Kh[...]texto impreso
Junge, M. ; Pérez García, David ; Palazuelos Cabezón, Carlos ; Villanueva, Ignacio ; Wolf, Michael | Springer | 2010In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order $\sqrt{n}$ (up to a logarithmic factor) when observables with n possible outcomes are used. A central tool[...]
