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Aron, Richard M. ; Pérez García, David ; Seoane-Sepúlveda, Juan B. | Polish Acad Sciencies Inst Mathematics | 2006We show that, given a set E subset of T of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t is an element of E is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely gen[...]texto impreso
Wolf, Michael M. ; Cubitt, Toby S. ; Pérez García, David | 2011-11-23This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of entanglement t[...]texto impreso
Brandao Fischer, Bruno ; Cubitt, Toby S. ; Lucia, Ángelo ; Michalakis, Spyridon ; Pérez García, David | American Institute of Physics | 2015We prove an area law with a logarithmic correction for the mutual information for fixed points of local dissipative quantum system satisfying a rapid mixing condition, under either of the following assumptions: the fixed point is pure or the sys[...]texto impreso
Using tools from classical signal processing, we show how to determine the dimensionality of a quantum system as well as the effective size of the environment's memory from observable dynamics in a model-independent way. We discuss the dependenc[...]texto impreso
Using tools from classical signal processing, we show how to determine the dimensionality of a quantum system as well as the effective size of the environment's memory from observable dynamics in a model-independent way. We discuss the dependenc[...]texto impreso
Wolf, Michael ; Pérez García, David ; Salles, Alejo ; Cavalcanti, Daniel ; Acin, Antonio | Rinton Press | 2010We provide a framework for Bell inequalities which is based on multilinear contractions. The derivation of the inequalities allows for an intuitive geometric depiction and their violation within quantum mechanics can be seen as a direct conseque[...]texto impreso
Bohr showed that the width of the strip (in the complex plane) on which a given Dirichlet series Sigma a(n)/n(s), s is an element of C, converges uniformly but not absolutely, is at most 1/2, and Bohnenblust-Hille that this bound in general is o[...]texto impreso
Sanz, Mikel ; Pérez García, David ; Cirac, Juan I. ; Wolf, Michael ; González Guillén, Carlos Eduardo | 2009We show that two different tensors defining the same translational invariant injective Projected Entangled Pair State (PEPS) in a square lattice must be the same up to a trivial gauge freedom. This allows us to characterize the existence of any [...]texto impreso
We show that two different tensors defining the same translational invariant injective projected entangled pair state (PEPS) in a square lattice must be the same up to a trivial gauge freedom. This allows us to characterize the existence of any [...]texto impreso
We construct a one-dimensional (1D) spin chain Hamiltonian with generic interactions and prove that the thermal correlation functions of the model admit an explicit random matrix representation. As an application of the result, we show how the o[...]texto impreso
We give a classification of gapped quantum phases of one-dimensional systems in the framework of matrix product states (MPS) and their associated parent Hamiltonians, for systems with unique as well as degenerate ground states and in both the ab[...]texto impreso
We prove that the composition S(u(1),..., u(n)) of a multilinear multiple 2-summing operator S with 2-summing linear operators u(j) is nuclear, generalizing a linear result of Grothendieck.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
Saberi, Hamed ; Weichselbaum, Andreas ; Lamata, Lucas ; Pérez García, David ; Delft, Jan von ; Solano, Enrique | American Physical Society | 2009We demonstrate how the matrix-product state formalism provides a flexible structure to solve the constrained optimization problem associated with the sequential generation of entangled multiqubit states under experimental restrictions. We consid[...]texto impreso
Fernández González, Carlos ; Mong, R. S. K. ; Pérez García, David ; Schuch, Norbert | American Physical Society | 2016Symmetrization of topologically ordered wave functions is a powerful method for constructing new topological models. Here we study wave functions obtained by symmetrizing quantum double models of a group G in the projected entangled pair states [...]
