The g-theorem and quantum information theory

We study boundary renormalization group flows between boundary conformal field theories in $1+1$ dimensions using methods of quantum information theory. We define an entropic $g$-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this $g$-function decreases along boundary renormalization group flows. This entropic $g$-theorem is valid at zero temperature, and is independent from the $g$-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.Comment: 34 pages + appendices, 8 figures. v2. Improved and corrected version of the proo

Visual-based Guidance System for a 6-DOF Robot

The idea of this bachelor’s thesis is to develop a position-based visual servoing system with two webcams that allows an anthropomorphic robot ABB IRB 120 with six degrees of freedom (DOF) to be guided in real time by an operator, by triangulating a specific target moved within the field of view (FOV) of a machine vision system. For this kind of motion control based on visual data input, termed visual servoing control, we need a stereo vision system to acquire the images of the target since three-dimensional information is required to perform object tracking with six DOF. These images are processed by a MATLAB ap-plication running in a remote PC. The current coordinates of the target referred to the left camera reference frame are extracted from the images and sent through an Ethernet connec-tion to the robot controller, which is programmed to receive the vectors and move its tool centre point (TCP) to the demanded position within its workspace.Grado en Ingeniería en Electrónica Industrial y Automátic

The entropic gg-theorem in general spacetime dimension

We establish the irreversibility of renormalization group flows on a pointlike defect inserted in a $d$-dimensional Lorentzian conformal field theory. We identify the impurity entropy $g$ with the quantum relative entropy in two equivalent ways. One involves a null deformation of the Cauchy surface, and the other is given in terms of a local quench protocol. Positivity and monotonicity of the relative entropy imply that $g$ decreases monotonically along renormalization group flows, and provides a clear information-theoretic meaning for this irreversibility.Comment: v2: minor corrections, matches published version. 6 pages, 2 figure

Irreversibility, QNEC, and defects

We first present an analysis of infinitesimal null deformations for the entanglement entropy, which leads to a major simplification of the proof of the $C$, $F$ and $A$-theorems in quantum field theory. Next, we study the quantum null energy condition (QNEC) on the light-cone for a CFT. Finally, we combine these tools in order to establish the irreversibility of renormalization group flows on planar $d$-dimensional defects, embedded in $D$-dimensional conformal field theories. This proof completes and unifies all known defect irreversibility theorems for defect dimensions $d\le 4$. The F-theorem on defects ($d=3$) is a new result using information-theoretic methods. For $d \ge 4$ we also establish the monotonicity of the relative entropy coefficient proportional to $R^{d-4}$. The geometric construction connects the proof of irreversibility with and without defects through the QNEC inequality in the bulk, and makes contact with the proof of strong subadditivity of holographic entropy taking into account quantum corrections.Comment: 26 pages, 1 figur

Irreversibility in quantum field theories with boundaries

We study conformal field theories with boundaries, and their boundary renormalization group (RG) flows, using methods from quantum information theory. Positivity of the relative entropy, together with unitarity and Lorentz invariance, give rise to bounds that characterize the irreversibility of such flows. This generalizes the recently proved entropic g-theorem to higher dimensions. In 2 + 1 dimensions with a boundary, we prove the entropic b-theorem — the decrease of the two-dimensional Weyl anomaly under boundary RG flows. In higher dimensions, the bound implies that the leading area coefficient of the entanglement entropy induced by the defect decreases along the flow. Our proof unifies these properties, and provides an information-theoretic interpretation in terms of the distinguishability between the short distance and long distance states. Finally, we establish a sum rule for the change in the area term in theories with boundaries, which could have implications for models with localized gravity.Fil: Casini, Horacio German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Salazar, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Torroba, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentin

Data-driven Loop Closure Detection in Bathymetric Point Clouds for Underwater SLAM

Simultaneous localization and mapping (SLAM) frameworks for autonomous navigation rely on robust data association to identify loop closures for back-end trajectory optimization. In the case of autonomous underwater vehicles (AUVs) equipped with multibeam echosounders (MBES), data association is particularly challenging due to the scarcity of identifiable landmarks in the seabed, the large drift in dead-reckoning navigation estimates to which AUVs are prone and the low resolution characteristic of MBES data. Deep learning solutions to loop closure detection have shown excellent performance on data from more structured environments. However, their transfer to the seabed domain is not immediate and efforts to port them are hindered by the lack of bathymetric datasets. Thus, in this paper we propose a neural network architecture aimed to showcase the potential of adapting such techniques to correspondence matching in bathymetric data. We train our framework on real bathymetry from an AUV mission and evaluate its performance on the tasks of loop closure detection and coarse point cloud alignment. Finally, we show its potential against a more traditional method and release both its implementation and the dataset used

Roadmap on optical security

Information security and authentication are important challenges facing our society. Recent attacks by hackers on the databases of large commercial and financial companies have demonstrated that more research and developments of advanced approaches are necessary to deny unauthorized access to critical data. Free space optical technology has been investigated by many researchers in information security, encryption, and authentication. The main motivation for using optics and photonics for information security is that optical waveforms possess many complex degrees of freedom such as amplitude, phase, polarization, large bandwidth, nonlinear transformations, quantum properties of photons, and multiplexing that can be combined in many ways to make the information encryption more secure and more difficult to attack. This roadmap article presents an overview of the potential, recent advances, and the challenges of optical security and encryption using free space optics. The roadmap on optical security is comprised of six categories that together include 16 short sections written by authors who have made relevant contributions in this field. The first category of this roadmap describes novel encryption approaches, including secure optical sensing which summarizes double random phase encryption applications and flaws [Yamaguchi], digital holographic encryption in free space optical technique which describes encryption using multidimensional digital holography [Nomura], simultaneous encryption of multiple signals [Pérez-Cabré], asymmetric methods based on information truncation [Nishchal], and dynamic encryption of video sequences [Torroba]. Asymmetric and one-way cryptosystems are analyzed by Peng. The second category is on compression for encryption. In their respective contributions, Alfalou and Stern propose similar goals involving compressed data and compressive sensing encryption. The very important area of cryptanalysis is the topic of the third category with two sections: Sheridan reviews phase retrieval algorithms to perform different attacks, whereas Situ discusses nonlinear optical encryption techniques and the development of a rigorous optical information security theory. The fourth category with two contributions reports how encryption could be implemented in the nano- or microscale. Naruse discusses the use of nanostructures in security applications and Carnicer proposes encoding information in a tightly focused beam. In the fifth category, encryption based on ghost imaging using single-pixel detectors is also considered. In particular, the authors [Chen, Tajahuerce] emphasize the need for more specialized hardware and image processing algorithms. Finally, in the sixth category, Mosk and Javidi analyze in their corresponding papers how quantum imaging can benefit optical encryption systems. Sources that use few photons make encryption systems much more difficult to attack, providing a secure method for authentication

Data-driven Approaches to Uncertainty Modelling for SLAM in the Open Sea

Autonomous underwater vehicles (AUVs) equipped with multibeam echo-sounders have become indispensable tools for bathymetric mapping due to their ability to reach seabed regions inaccessible to surface vessels. However, the closer proximity to the survey area comes at the expense of a growing error in the AUV global pose estimate due to the lack of prior maps or a geo-referencing system underwater, such as GPS. This limitation, together with the changing environment dynamics in deep sea waters and the scale of the areas to map, makes simultaneous localization and mapping (SLAM) a necessary enabler for long-range, reliable and safe AUV navigation in open sea missions.SLAM has allowed the safe deployment of self-driving cars on the streets and service robots in our homes, but remains a challenge in the deep sea domain. This is due to the constrained sensing capabilities available underwater and the scarcity of distinguishable features in the seabed. As a result of these, successful place recognition is infrequent, yielding loop closure (LC) detections more sparse and therefore more crucial. To adequately factor in each LC constraint in a SLAM back-end, their uncertainties need to be carefully parameterized to weight their influence in the final AUV trajectory estimate. Thus, this thesis is concerned with modelling these uncertainties, in particular when analytical models cannot be derived, focusing instead in data-driven methods.  We present our contributions in three key SLAM areas targeting this problem. First, our work on inferring the uncertainties in the bathymetric submap registration process shows how deep learning techniques can be successfully applied to learning noise models directly from raw data and without ground truth position information. We further show how the predicted uncertainties improve the convergence of submap-based graph-SLAM solutions in AUV surveys.Secondly, we introduce a methodology to construct terrain representations with Stochastic Variational Gaussian processes (SVGP) propagating the AUV localization and sensors uncertainties into the final maps. The proposed approach is not limited to any GP kernel or noise model in the data and can handle datasets of millions of training points. The experiments demonstrate how the learned terrain models yield improved particle filter estimates in AUV localization problems.Finally, we adapt the previous SVGP mapping approach to online bathymetric learning and demonstrate its scalability and flexibility in a Rao-Blackwellized SLAM framework. The presented RBPF-SVGP solution is capable of maintaining up to 100 particles in parallel, each with a single SVGP map capable of regressing entire surveys. Our results show how the RBPF-SVGP can perform in real time in an embedded platform and can be executed live in an AUV. Additionally, all the implementations proposed have been made publicly available to promote further research in underwater SLAM and the adoption of common open-source frameworks, datasets and benchmarks in the field.Autonoma undervattensfarkoster (AUV) utrustade med multibeam-ekolod har blivit ett oumbärligt verktyg för batymetrisk kartläggning tack vare dess förmåga att nå hahvsbottenområden som är oåtkomliga för ytfartyg.Fördelen med att kunna komma närmare till undersökningsområden kommer dock på bekostnad av ett växande fel i AUVs globala positionsuppskattning, detta på grund av bristen på tidigare kartor eller undervattens-georeferenssystem, såsom GPS.Denna begränsning, tillsammans med förändrande vattendynamik i djuphavsvatten och skalan på områden som ska kartläggas, gör att Simultaneous Localization and Mapping (SLAM) är ett måste för pålitlig och säker AUV-navigering i öppet hav för långa avstånd. SLAM har möjliggjort säker utplacering av självkörande bilar på gator och servicerobotar i våra hem, men i djuphavsområdet är SLAM fortfarande en utmaning.Detta beror på de begränsade avkänningsmöjligheterna tillgängliga under vatten och avsaknaden på urskiljbara kännetecken i havsbotten.På grund av detta är lyckad platsigenkänning sällsynt, vilket leder till färre detektion av loop closure (LC). Varje LC blir därmed mer avgörande.För att korrekt kunna lägga in LC-begränsningar i en SLAM-backend måste deras osäkerheter noggrant parametriseras för att väga deras inflytande i den slutliga uppskattningen av AUVs kurs.Denna doktorsavhandling handlar därför om modellering av dessa osäkerheter och fokuset ligger på datadrivna metoder i tillfällen där analytiska modeller inte kan härledas. Vi presenterar våra bidrag inom tre nyckelområden för SLAM med hänsyn till detta problem.För det första visar vårt arbete med att härleda osäkerheter i den batymetriska kartregistreringsprocessen hur djupinlärningstekniker kan tillämpas för att lära sig brusmodeller direkt från rådata och utan ground truth positionsinformation.Vidare visar vi hur de förutspådda osäkerheterna förbättrar konvergensen av submap-baserad graf-SLAM lösningar i AUV kartläggningar.För det andra introducerar vi en metodik för att konstruera terrängrepresentationer där Stochastic Variational Gaussian processes (SVGP) används för att sprida AUVs lokaliserings- och sensorosäkerheter till de slutliga batymetriska kartorna.Den föreslagna metodiken är inte begränsad till någon GP-kärna eller brusmodell i data och kan hantera dataset med miljontals träningspunkter.Experimenten visar hur de lärda terrängmodellerna förbättrar partikelfilteruppskattningar av AUV-lokalisering.Slutligen anpassar vi den tidigare nämnda SVGP-kartläggningsmetoden till online batymetriskinlärning och visar dess skalbarhet och flexibilitet i ett Rao-Blackwellized SLAM-ramverk.Den presenterade RBPF-SVGP lösningen kan köras med upp till 100 partiklar parallellt, där varje ensklid partikel har sin egen SVGP-karta över hela kartläggningsområden.Våra resultat visar hur RBPF-SVGP kan tillämpas i realtid i en inbyggd plattform och kan utföras live i en AUV. Vidare har alla föreslagna implementeringar gjorts allmänt tillgängliga för att främja vidare forskning inom undervattens-SLAM och antagande av gemensamma ramverk med öppen källkod, dataset och benchmark inom forskningsområdet.QC 20221128</p