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Autor Pérez García, David |
Documentos disponibles escritos por este autor (74)
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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 [...]texto impreso
We prove that every countably additive polymeasure can be decomposed in a unique way as the sum of a "discrete" polymeasure plus a "continuous" polymeasure. This generalizes a previous result of Saeki.texto impreso
Masanes, Lluís ; Müller, M.P. ; Pérez García, David ; Augusiak, Remigiusz | American Institute of Physics | 2014-12We consider a very natural generalization of quantum theory by letting the dimension of the Bloch ball be not necessarily three. We analyze bipartite state spaces where each of the components has a d-dimensional Euclidean ball as state space. In[...]texto impreso
Cadarso, Andrea ; Sanz, Mikel ; Wolf, Michael M. ; Cirac, J.I. ; Pérez García, David | American Physical Society | 2013-01Based on the theory of Matrix Product States, we give precise statements and complete analytical proofs of the following claim: a large fractionalization in the magnetization or the need of long-range interactions imply large entanglement in the[...]texto impreso
Masanes, Lluís ; Muller, Markus P. ; Augusiak, Remigiusz ; Pérez García, David | National Academy of Sciences | 2013-10Does information play a significant role in the foundations of physics? Information is the abstraction that allows us to refer to the states of systems when we choose to ignore the systems themselves. This is only possible in very particular fra[...]texto impreso
Fernández González, C. ; Schuch, N. ; Wolf, M.M. ; Cirac, J.I. ; Pérez García, David | Springer | 2015-01For every Matrix Product State (MPS) one can always construct a so-called parent Hamiltonian. This is a local, frustration free, Hamiltonian which has the MPS as ground state and is gapped. Whenever that parent Hamiltonian has a degenerate groun[...]texto impreso
De las Cuevas, G. ; Cubitt, J.L. ; Wolf, M.M. ; Pérez García, David | American Institute of Physics Inc. | 2016We show a fundamental limitation in the description of quantum many-body mixed states with tensor networks in purification form. Namely, we show that there exist mixed states which can be represented as a translationally invariant (TI) matrix pr[...]texto impreso
Fernández González, Carlos ; Schuch, Norbert ; Wolf, Michael M. ; Cirac, J.I. ; Pérez García, David | American Physical Society | 2012-12We study Hamiltonians which have Kitaev's toric code as a ground state, and show how to construct a Hamiltonian which shares the ground space of the toric code, but which has gapless excitations with a continuous spectrum in the thermodynamic li[...]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
Pérez García, David | Universidad Nacional de Colombia - Sede Bogotá - Facultad de Artes - Instituto de Investigaciones Hábitat, Ciudad & Territorio | 2017-12-01La epistemología del diseño ha sido objeto de numerosos debates. En este trabajo se expondrá la posibilidad de entender que el diseño tiene una especificidad que no se puede confundir con otro aspecto de las actividades humanas como la ciencia, [...]texto impreso
Cooney, Tom ; Junge, Marius ; Navascués Cobo, Miguel ; Pérez García, David ; Villanueva, Ignacio | Springer | 2013Bipartite correlations generated by non-signalling physical systems that admit a finite-dimensional local quantum description cannot exceed the quantum limits, i.e., they can always be interpreted as distant measurements of a bipartite quantum s[...]texto impreso
Junemann, J. ; Cadarso, A. ; Pérez García, David ; Bermúdez, A. ; García Ripoll, Juan José | American Physical Society | 2013-12-06We derive a Lieb-Robinson bound for the propagation of spin correlations in a model of spins interacting through a bosonic lattice field, which satisfies a Lieb-Robinson bound in the absence of spin-boson couplings. We apply these bounds to a sy[...]texto impreso
Castillo, J.M.F. ; García, R. ; Defant, A. ; Pérez García, David ; Suárez, J. | Cambridge Phylosophical Society | 2012-01We study different aspects of the connections between local theory of Banach spaces and the problem of the extension of bilinear forms from subspaces of Banach spaces. Among other results, we prove that if X is not a Hilbert space then one may f[...]texto impreso
By using random matrix models, we uncover a connection between the low-energy sector of four-dimensional QCD at finite volume and the Heisenberg XX model in a 1D spin chain. This connection allows us to relate crucial properties of QCD with phys[...]texto impreso
We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fi[...]texto impreso
Using random matrix techniques and the theory of Matrix Product States we show that reduced density matrices of quantum spin chains have generically maximum entropy.texto impreso
Matrix product vectors form the appropriate framework to study and classify one-dimensional quantum systems. In this work, we develop the structure theory of matrix product unitary operators (MPUs) which appear e.g. in the description of time ev[...]texto impreso
We introduce schemes for quantum computing based on local measurements on entangled resource states. This work elaborates on the framework established in Gross and Eisert [Phys. Rev. Lett. 98, 220503 (2007); quant-ph/0609149]. Our method makes u[...]texto impreso
It is well known that jointly measurable observables cannot lead to a violation of any Bell inequality-independent of the state and the measurements chosen at the other site. In this Letter we prove the converse: every pair of incompatible quant[...]texto impreso
Villanueva, Ignacio ; Bombal Gordón, Fernando ; Pérez García, David | Oxford University Press | 2004We introduce a new class of multilinear p-summing operators, which we call multiple p-summing. Using them, we can prove several multilinear generalizations of Grothendieck’s “fundamental theorem of the metric theory of tensor products”. Several [...]texto impreso
In this paper, we improve some previous results about multiple p-summing multilinear operators by showing that every multilinear form from spaces is multiple p-summing for 1 p 2. The proof is based on the existence of a predual for the Banach s[...]texto impreso
In this paper, we characterize, for 1 ? ptexto impreso
Aron, R.M. ; García-Pacheco, F.J. ; Pérez García, David ; Seoane-Sepúlveda, Juan B. | Elsevier | 2009A subset M of a topological vector space X is said to be dense-lineable in X if there exists an infinite dimensional linear manifold in M boolean OR {0} and dense in X. We give sufficient conditions for a lineable set to be dense-lineable, and w[...]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
Haegeman, Jutho ; Pérez García, David ; Cirac, Ignacio ; Schuch, Norbert | American Physical Society | 2012-08-03We introduce an order parameter for symmetry-protected phases in one dimension which allows us to directly identify those phases. The order parameter consists of stringlike operators and swaps, but differs from conventional string order operator[...]texto impreso
We show that, for every orthogonally additive homogeneous polynomial P on a space of continuous functions C(K) with values in a Banach space Y, there exists a linear operator S : C(K) -> Y such that P(f) = S(f(n)). This is the C(K) version of a[...]texto impreso
Schuch, Norbert ; Pérez García, David ; Cirac, Ignacio | 2010We introduce a framework for characterizing Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) in terms of symmetries. This allows us to understand how PEPS appear as ground states of local Hamiltonians with finitely degenera[...]texto impreso
In this paper we consider projected entangled pair states (PEPS) on arbitrary lattices. We construct local parent Hamiltonians for each PEPS and isolate a condition under which the state is the unique ground state of the Hamiltonian. This condit[...]texto impreso
Tsirelson's problem deals with how to model separate measurements in quantum mechanics. In addition to its theoretical importance, the resolution of Tsirelson's problem could have great consequences for device independent quantum key distributio[...]texto impreso
Schwarz, Martin ; Temme, Kristan ; Verstraete, Frank ; Pérez García, David ; Cubitt, Toby Stanley | American Physical Society | 2013-09Simulating exotic phases of matter that are not amenable to classical techniques is one of the most important potential applications of quantum information processing. We present an efficient algorithm for preparing a large class of topological [...]texto impreso
Scarpa, G. ; Molnár, Andras ; Gé, Y. ; García-Ripoll, J.J. ; Schuch, N. ; Pérez García, David ; Iblisdir, S. | American Physical Society | 2020-11-20Matrix product states and projected entangled pair states (PEPS) are powerful analytical and numerical tools to assess quantum many-body systems in one and higher dimensions, respectively. While matrix product states are comprehensively understo[...]texto impreso
Cuevas, Gemma de las ; Schuch, Norbert ; Pérez García, David ; Cirac, J.I. | IOP Publishing | 2013-12-10We analyze the description of quantum many-body mixed states using matrix product states and operators. We consider two such descriptions: (i) as a matrix product density operator of bond dimension D; and (ii) as a purification that is written a[...]texto impreso
Pérez García, David | 2009Quantum Information is the science that aims to use the unusual behavior of the microscopic world, governed by the laws of Quantum Mechanics, in order to improve the way in which we compute or communicate information. Though the first ideas in t[...]texto impreso
In non-relativistic quantum mechanics, measurements performed by separate observers are modeled via tensor products. In Algebraic Quantum Field Theory, though, local observables corresponding to space-like separated parties are just required to [...]texto impreso
In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found. Using th[...]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
Lucia, Ángelo ; Cubitt, Toby S. ; Michalakis, Spyridon ; Pérez García, David | American Physical Society | 2014-09-27The physics of many materials is modeled by quantum many-body systems with local interactions. If the model of the system is sensitive to noise from the environment, or small perturbations to the original interactions, it will not model properly[...]texto impreso
Schuch, Norbert ; Poilblanc, Didier ; Cirac, Juan I. ; Pérez García, David | American Physical Society | 2012-09We study resonating valence bond (RVB) states in the projected entangled pair states (PEPS) formalism. Based on symmetries in the PEPS description, we establish relations between the toric code state, the orthogonal dimer state, and the SU(2) si[...]texto impreso
Cirac, J. Ignacio ; Michalakis, Spyridon ; Pérez García, David ; Schuch, Norbert | American Physical Society | 2013-09-06We analyze a criterion which guarantees that the ground states of certain many-body systems are stable under perturbations. Specifically, we consider PEPS, which are believed to provide an efficient description, based on local tensors, for the l[...]texto impreso
Iblisdir, I. ; Pérez García, David ; Aguado, M. ; Pachos, J. | American Physical Society | 2009-04-16Understanding the behavior of topologically ordered lattice systems at finite temperature is a way of assessing their potential as fault-tolerant quantum memories. We compute the natural extension of the topological entanglement entropy for T> 0[...]texto impreso
Lamata, L. ; León, J. ; Pérez García, David ; Salgado, D. ; Solano, E. | American Physical Society | 2008-10-31We study the possibility for a global unitary applied on an arbitrary number of qubits to be decomposed in a sequential unitary procedure, where an ancillary system is allowed to interact only once with each qubit. We prove that sequential unita[...]texto impreso
We study scenarios where a finite set of non-demolition von-Neumann measurements are available. We note that, in some situations, repeated application of such measurements allows estimating an infinite number of parameters of the initial quantum[...]texto impreso
Bañuls, M.C. ; Pérez García, David ; Wolf, M.M. ; Verstraete, F. ; Cirac, J.I. | American Physical Society | 2008Matrix product states can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system [Schon et al., Phys. Rev. Lett. 95, 110503 (2005)]. We introduce a family of states that extends this definition [...]texto impreso
Cubitt, Toby S. ; Lucia, Ángelo ; Michalakis, Spyridon ; Pérez García, David | Springer | 2015-08-29Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. In the setting of quantum many-body systems on a la[...]texto impreso
Pérez García, David ; Wolf, M.M. ; Sanz, M. ; Verstraete, F. ; Cirac, J.I. | The American Physical Society | 2008-04-25We show that the existence of string order in a given quantum state is intimately related to the presence of a local symmetry by proving that both concepts are equivalent within the framework of finitely correlated states. Once this connection i[...]texto impreso
This is the supplementary information associated to the article: T.S. Cubitt, D. Perez-Garcia, M.M. Wolf, Undecidability of the spectral gap, Nature 528, 207-211 (2015), doi:10.1038/nature16059texto impreso
Topological ordered phases are related to changes in the properties of their quasiparticle excitations (anyons). We study these relations in the framework of projected entanglement pair states and show how condensing and confining anyons reduces[...]texto impreso
What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the study of quantum nonlocality, we develop a math[...]texto impreso
Wolf, Michael ; Pérez García, David | 2010Given a list of n complex numbers, when can it be the spectrum of a quantum channel, i.e., a completely positive trace preserving map? We provide an explicit solution for the n=4 case and show that in general the characterization of the non-zero[...]texto impreso
We prove that the only rearrangement invariant (r.i.) spaces for which there exists a crossnorm verifying that the tensor product of these spaces preserves the "natural" r.i. space structure, in the sense that it makes the multiplication operato[...]texto impreso
A study of the thermal properties of two-dimensional topological lattice models is presented. This work is relevant to assess the usefulness of these systems as a quantum memory. For our purposes, we use the topological mutual information I(topo[...]texto impreso
Poilblanc, Didier ; Schuch, Norbert ; Pérez García, David ; Cirac, J. Ignacio | American Physical Society | 2012-07-06We examine in details the connections between topological and entanglement properties of short-range resonating valence bond (RVB) wave functions using projected entangled pair states (PEPS) on kagome and square lattices on (quasi)infinite cylin[...]texto impreso
Schuch, Norbert ; Poilblanc, Didier ; Cirac, J.I. ; Pérez García, David | American Physical Society | 2013We study the structure of topological phases and their boundaries in the projected entangled-pair states (PEPS) formalism. We show how topological order in a system can be identified from the structure of the PEPS transfer operator and subsequen[...]texto impreso
Villanueva, Ignacio ; Junge, Marius ; Pérez García, David ; Wolf, Michael ; Palazuelos Cabezón, Carlos | Springer | 2008We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount [...]texto impreso
Villanueva, Ignacio ; Junge, Marius ; Pérez García, David ; Wolf, Michael ; Palazuelos Cabezón, Carlos | Springer | 2010-12In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order ?(?n?Log2n) when observables with n possible outcomes are used. A central tool in the analysis is a close[...]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[...]texto impreso
Villanueva, Ignacio ; Pérez García, David | Matematisk Institut, Universitetsparken NY Munkegade | 2005We prove that a tensor norm alpha (defined on tensor products of Hilbert spaces) is the Hilbert-Schmidt norm if and only if l(2) circle times(...)circle times l(2), endowed with the norm alpha, has an unconditional basis. This extends a classica[...]texto impreso
The spectral gap-the energy difference between the ground state and first excited state of a system-is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, the question of the existence of gapped [...]texto impreso
Villanueva, Ignacio ; Pérez García, David ; Cabello Sánchez, Félix | Oxford University Press | 2006-10We describe complemented Copies Of l(2) both in C(K-1)circle times C-pi(K-2) when at least one of the compact spaces K-i is not scattered and in L-1(mu(1))circle times L-is an element of(1)(mu(2)) when at least one of the measures is not atomic.[...]texto impreso
Using a ‘reasonable’ measure in , the space of 2-homogeneous polynomials on ?1n, we show the existence of a set of positive (and independent of n) measure of polynomials which do not attain their norm at the vertices of the unit ball of ?1n. Ne[...]