Person:
Palazuelos Cabezón, Carlos

First Name

Carlos

Last Name

Palazuelos Cabezón

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Matemáticas

Department

Análisis Matemático Matemática Aplicada

Area

Análisis Matemático

Identifiers

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Now showing 1 - 10 of 30

Hahn–Banach extension of multilinear forms and summability
(Academic Press, 2007-12-15) Jarchow , Hans; Palazuelos Cabezón, Carlos; Pérez García, David; Villanueva, Ignacio
The 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 occurs when we consider Banach spaces which have the property that every bilinear form extends to any superspace.
The natural rearrangement invariant structure on tensor products
(Elsevier, 2008) Fernández González, Carlos; Palazuelos Cabezón, Carlos; Pérez García, David
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 operator B a topological isomorphism, are the Lp spaces.
Survey on nonlocal games and operator space theory.
(American Institute of Physics, 2016) Palazuelos Cabezón, Carlos; Vidick, Thomas
This review article is concerned with a recently ncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.
Reducing the number of questions in nonlocal games
(American Institute of Physics Inc., 2016) Junge, M.; Oikhberg, T.; Palazuelos Cabezón, Carlos
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 β*(G)/β(G) of the quantum over the classical bias. We apply our method to the Khot-Vishnoi game, with exponentially many questions per player, to produce a family of games indexed in n with polynomially many (N ≈ n8) questions and n answers per player so that the ratio of the quantum over the classical bias is Ω(n/log2 n).
On the relation between completely bounded and (1, cb)- summing maps with applications to quantum xor games
(Elsevier, 2022-09-13) Junge, Marius; Kubicki, Alexander M.; Palazuelos Cabezón, Carlos; Villanueva, Ignacio
In this work we show that, given a linear map from a general operator space into the dual of a C∗ -algebra, its completely bounded norm is upper bounded by a universal constant times its (1, cb)-summing norm. This problem is motivated by the study of quantum XOR games in the field of quantum information theory. In particular, our results imply that for such games entangled strategies cannot be arbitrarily better than those strategies using one-way classical communication.
Sampling Quantum Nonlocal Correlations with High Probability
(Springer, 2016) González-Guillén, C.E.; Jimenez, C.H.; Palazuelos Cabezón, Carlos; Villanueva, Ignacio
It is well known that quantum correlations for bipartite dichotomic measurements are those of the form (Formula presented.), where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of (Formula presented.), where the previous vectors are sampled according to the Haar measure in the unit sphere of (Formula presented.). In particular, we prove the existence of an (Formula presented.) such that if (Formula presented.), (Formula presented.) is nonlocal with probability tending to 1 as (Formula presented.), while for (Formula presented.), (Formula presented.) is local with probability tending to 1 as (Formula presented.).
Channel capacities via p-summing norms
(Elsevier, 2015-02-26) Junge, Marius; Palazuelos Cabezón, Carlos
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 fully generalized to the quantum setting, and revealed qualitatively new phenomena in comparison. In this paper we consider the classical capacity of quantum channels with restricted assisted entanglement. These capacities include the classical capacity and the unlimited entanglement-assisted classical capacity of a quantum channel. Our approach to restricted capacities is based on tools from functional analysis, and in particular the notion of p-summing maps going back to Grothendieck’s work. Pisier’s noncommutative vector-valued Lp spaces allow us to establish the new connection between functional analysis and information theory in the quantum setting.
Maximal gap between local and global distinguishability of bipartite quantum states
(2021) Corrêa, William H. G.; Lami, Ludovico; Palazuelos Cabezón, Carlos
We prove a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements (without classical communication) at discriminating any two bipartite quantum states. Our result implies, for example, that any two orthogonal quantum states of a nA×nB bipartite quantum system can be discriminated via local measurements with an error probability no larger than 1/2 (1 − 1/ cmin{nA,nB}, where 1 ≤ c ≤ 2√2 is a universal constant, and our bound scales provably optimally with the local dimensions nA, nB. Mathematically, this is achieved by showing that the distinguishability norm ||·||LO associated with local measurements satisfies that ||·||≤ 2√2min{nA, nB} ||·|LO, where ||·||1 is the trace norm.
Euclidean Distance Between Haar Orthogonal and Gaussian Matrices
(Springer New York LLC, 2016) González Guillén, Carlos Eduardo; Palazuelos Cabezón, Carlos; Villanueva, Ignacio
In 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 the Gram–Schmidt orthonormalization procedure by columns to obtain a Haar-distributed orthogonal matrix (Formula presented.). If (Formula presented.) denotes the vector formed by the first m-coordinates of the ith row of (Formula presented.) and (Formula presented.), our main result shows that the Euclidean norm of (Formula presented.) converges exponentially fast to (Formula presented.), up to negligible terms. To show the extent of this result, we use it to study the convergence of the supremum norm (Formula presented.) and we find a coupling that improves by a factor (Formula presented.) the recently proved best known upper bound on (Formula presented.). Our main result also has applications in Quantum Information Theory.
Genuine multipartite entanglement of quantum states in the multiple-copy scenario
(2022-06-13) Palazuelos Cabezón, Carlos; Vicente, Julio I. de
Genuine multipartite entanglement (GME) is considered a powerful form of entanglement since it corresponds to those states that are not biseparable, i.e. a mixture of partially separable states across different bipartitions of the parties. In this work we study this phenomenon in the multiple-copy regime, where many perfect copies of a given state can be produced and controlled. In this scenario the above definition leads to subtle intricacies as biseparable states can be GME-activatable, i.e. several copies of a biseparable state can display GME. We show that the set of GMEactivatable states admits a simple characterization: a state is GME-activatable if and only if it is not partially separable across one bipartition of the parties. This leads to the second question of whether there is a general upper bound in the number of copies that needs to be considered in order to observe the activation of GME, which we answer in the negative. In particular, by providing an explicit construction, we prove that for any number of parties and any number k 2 N there exist GME-activatable multipartite states of fixed (i.e. independent of k) local dimensions such that k copies of them remain biseparable.