Memory effects can make the transmission capability of a communication channel uncomputable

Most communication channels are subjected to noise. One of the goals of Information Theory is to add redundancy in the transmission of information so that the information is transmitted reliably and the amount of information transmitted through the channel is as large as possible. The maximum rate at which reliable transmission is possible is called the capacity. If the channel does not keep memory of its past, the capacity is given by a simple optimization problem and can be efficiently computed. The situation of channels with memory is less clear. Here we show that for channels with memory the capacity cannot be computed to within precision 1/5. Our result holds even if we consider one of the simplest families of such channels -information-stable finite state machine channels-, restrict the input and output of the channel to 4 and 1 bit respectively and allow 6 bits of memory.Comment: Improved presentation and clarified claim

Chern-Simons theory encoded on a spin chain

We construct a 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 observables of $U(N)$ Chern-Simons theory on $S^{3}$ can be reproduced with the thermal correlation functions of the 1d spin chain, which is of the XX type, with a suitable choice of exponentially decaying interactions between infinitely many neighbours. We show that for this model, the correlation functions of the spin chain at a finite temperature $\beta =1$ give the Chern-Simons partition function, quantum dimensions and the full topological $S$-matrix.Comment: v2, 11 pages. Expanded, more detailed version. Misprints correcte

Superadditivity of quantum relative entropy for general states

The property of superadditivity of the quantum relative entropy states that, in a bipartite system $\mathcal{H}_{AB}=\mathcal{H}_A \otimes \mathcal{H}_B$, for every density operator $\rho_{AB}$ one has $D( \rho_{AB} || \sigma_A \otimes \sigma_B ) \ge D( \rho_A || \sigma_A ) +D( \rho_B || \sigma_B)$. In this work, we provide an extension of this inequality for arbitrary density operators $\sigma_{AB}$. More specifically, we prove that $\alpha (\sigma_{AB})\cdot D({\rho_{AB}}||{\sigma_{AB}}) \ge D({\rho_A}||{\sigma_A})+D({\rho_B}||{\sigma_B})$ holds for all bipartite states $\rho_{AB}$ and $\sigma_{AB}$, where $\alpha(\sigma_{AB})= 1+2 || \sigma_A^{-1/2} \otimes \sigma_B^{-1/2} \, \sigma_{AB} \, \sigma_A^{-1/2} \otimes \sigma_B^{-1/2} - \mathbb{1}_{AB} ||_\infty$.Comment: 14 pages. v3: Final version. The main theorem has been improved, adding a fourth step to its proof and also some remarks. v2: There was a flaw in the proof of the previous version. This has been corrected in this version. The constant appearing in the main Theorem has changed accordingl

Aggregating opinions in non-uniform ordered qualitative scales

Producción CientíficaThis paper introduces a new voting system in the setting of ordered qualitative scales. The process is conducted in a purely ordinal way by considering an ordinal proximity measure that assigns an ordinal degree of proximity to each pair of linguistic terms of the qualitative scale. Once the agents assess the alternatives through the qualitative scale, the alternatives are ranked according to the medians of the ordinal degrees of proximity between the obtained individual assessments and the highest linguistic term of the scale. Since some alternatives may share the same median, an appropriate tie-breaking procedure is introduced. Some properties of the proposed voting system have been provided.Ministerio de Economía, Industria y Competitividad (Project ECO2016-77900-P

Symmetry reduction induced by anyon condensation: a tensor network approach

Topological ordered phases are related to changes in the properties of their quasi-particle excitations (anyons). We study these relations in the framework of projected entanglement pair states (\textsf{PEPS}) and show how condensing and confining anyons reduces a local gauge symmetry to a global on-site symmetry. We also study the action of this global symmetry over the quasiparticle excitations. As a byproduct, we observe that this symmetry reduction effect can be applied to one-dimensional systems as well, and brings about appealing physical interpretations on the classification of phases with symmetries using matrix product states (\textsf{MPS}). The case of $\mathbb{Z}_2$ on-site symmetry is studied in detail.Comment: 21+5 pages, 15+3 figures. Introduction and conclusions enlarged, references and figure added, minor typos corrected, appendix about dyons adde

Mathematical open problems in Projected Entangled Pair States

Projected Entangled Pair States (PEPS) are used in practice as an efficient parametrization of the set of ground states of quantum many body systems. The aim of this paper is to present, for a broad mathematical audience, some mathematical questions about PEPS.Comment: Notes associated to the Santal\'o Lecture 2017, Universidad Complutense de Madrid (UCM), minor typos correcte

ALOJA: A benchmarking and predictive platform for big data performance analysis

The main goals of the ALOJA research project from BSC-MSR, are to explore and automate the characterization of cost-effectivenessof Big Data deployments. The development of the project over its first year, has resulted in a open source benchmarking platform, an online public repository of results with over 42,000 Hadoop job runs, and web-based analytic tools to gather insights about system's cost-performance1. This article describes the evolution of the project's focus and research lines from over a year of continuously benchmarking Hadoop under dif- ferent configuration and deployments options, presents results, and dis cusses the motivation both technical and market-based of such changes. During this time, ALOJA's target has evolved from a previous low-level profiling of Hadoop runtime, passing through extensive benchmarking and evaluation of a large body of results via aggregation, to currently leveraging Predictive Analytics (PA) techniques. Modeling benchmark executions allow us to estimate the results of new or untested configu- rations or hardware set-ups automatically, by learning techniques from past observations saving in benchmarking time and costs.This work is partially supported the BSC-Microsoft Research Centre, the Span- ish Ministry of Education (TIN2012-34557), the MINECO Severo Ochoa Research program (SEV-2011-0067) and the Generalitat de Catalunya (2014-SGR-1051).Peer ReviewedPostprint (author's final draft

Quantum Steering and Space-Like Separation

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 commute. The problem of determining whether these two definitions of "separation" lead to the same set of bipartite correlations is known in non-locality as Tsirelson's problem. In this article, we prove that the analog of Tsirelson's problem in steering scenarios is false. That is, there exists a steering inequality that can be violated or not depending on how we define space-like separation at the operator level.Comment: Some typos corrected. Short discussion about Algebraic Quantum Field Theory. Modified introduction and conclusio

Traducción y anotación “filológica”: calas en la poesía

This work explores the translation of some examples of the ancient Greek poetry. The focus point is the thought about the different changes and modes of poetics comprehension, as well as the purpose of the “philological” note, whose end is the understanding of the poetry.Este trabajo explora algunos ejemplos de traducción de poesía griega antigua, a fin de reflexionar sobre los distintos cambios y modos de recepción del contenido poético, así como la función de la nota “filológica” que busca hacer comprensible la traslación de la poesía en cuestión