Information Geometry of Entanglement Renormalization for free Quantum Fields

We provide an explicit connection between the differential generation of entanglement entropy in a tensor network representation of the ground states of two field theories, and a geometric description of these states based on the Fisher information metric. We show how the geometrical description remains invariant despite there is an irreducible gauge freedom in the definition of the tensor network. The results might help to understand how spacetimes may emerge from distributions of quantum states, or more concretely, from the structure of the quantum entanglement concomitant to those distributions.Comment: 18 pages. 1 eps figure. References added. Some comments adde

Entanglement Renormalization and Two Dimensional String Theory

The entanglement renormalization flow of a (1+1) free boson is formulated as a path integral over some auxiliary scalar fields. The resulting effective theory for these fields amounts to the dilaton term of non-critical string theory in two spacetime dimensions. A connection between the scalar fields in the two theories is provided, allowing to acquire novel insights into how a theory of gravity emerges from the entanglement structure of another one without gravity.Comment: 20 pages. v3 minor corrections. Accepted for publication in Physics Letters

A post-Gaussian approach to dipole symmetries and interacting fractons

We use a post-Gaussian variational approach to non-perturbatively study a general class of interacting bosonic quantum field theories with generalized dipole symmetries and fractonic behaviour. We find that while a Gaussian approach allows to carry out a consistent renormalization group (RG) flow analysis of these theories, this only grasps the interaction terms associated to the longitudinal motion of dipoles, which is consistent with previous analysis using large $N$ techniques. Remarkably, our post-Gaussian proposal, by providing a variational improved effective potential, is able to capture the transverse part of the interaction between dipoles in such a way that a non trivial RG flow for this term is obtained and analyzed. Our results suggest that dipole symmetries that manifest due to the strong coupling of dipoles, may robustly emerge at low energies from short distance models without that symmetry.Comment: 34 pages, 4 figures, 4 appendices. v2: some references added and two paragraphs rewritte

Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems

Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between different energy levels. We consider the quantum work distribution associated with the driving of chaotic quantum systems described by random matrix Hamiltonians and characterize exactly the work statistics associated with a sudden quench for arbitrary temperature and system size. Knowledge of the work statistics yields the Loschmidt echo dynamics of an entangled state between two copies of the system of interest, the thermofield double state. This echo dynamics is dictated by the spectral form factor. We discuss its relation to frame potentials and its use to assess information scrambling.Comment: 11+6pp, 5 figures. v3: version accepted for publication in Quantu

Una arquitectura neuronal de inspiración biológica para el aprendizaje y control del movimiento de agarre en plataformas robóticas antropomorfas

[SPA] En esta Tesis Doctoral se proponen y desarrollan nuevos modelos neuronales de inspiración biológica para el control y aprendizaje de tareas de agarre por parte de dispositivos robóticos antropomorfos. En la primera parte de la Tesis se lleva a cabo una revisión exhausta de los aspectos más relevantes del comportamiento humano y animal durante movimientos de agarre de objetos en la que se resaltan las características invariantes de dicho movimiento, establecidas a través de numerosos experimentos psicofísicos con humanos y primates. A continuación se realiza un repaso al estado actual del conocimiento relativo a la neurobiología que subyace a los comportamientos motrices descritos anteriormente. Con esta base, la Tesis presenta un modelo para la organización del movimiento de agarre que mimetiza las interacciones entre distintas áreas del córtex y los ganglios basales durante la planificación y ejecución del movimiento de agarre en condiciones normales y en condiciones de déficit motor parkinsoniano. El modelo genera trayectorias realistas de agarre a través de la computación y actualización continúa de las señales que codifican la diferencia entre los programas motores que se establecen para la realización de la tarea, y el estado actual de los efectores finales del movimiento involucrados en la ejecución de dicha tarea. Las principales hipótesis del modelo son: (1) el control del transporte de la mano y de la apertura de los dedos se lleva a cabo a través de la acción de señales de paso talámicas cuya modulación corre a cargo de los circuitos neuronales de los ganglios basales. Dichas señales permiten la ejecución coordinada de los distintos subobjetivos que componen una tarea de agarre. (2) La disrupción del programa motriz detectado en la enfermedad de Parkinson, se debe a la modificación en la funcionalidad de la red de interneuronas colinérgicas del estriado ante una deflexión de dopamina estriatal. En estas condiciones, dicha red de interneuronas pierde la habilidad para mantener segregada la información procesada en bucles cortico ganglio basles paralelos y como consecuencia se producen acoplamientos entre distintos canales cortico subcorticales que afectan a los patrones cinemáticos prototípicos del movimiento de agarre. (3) La aplicación de este modelo a un sistema en el que los efectores finales de los movimientos son antropomorficamente realistas, implica el desarrollo, a partir de los resultados de experiencias psicofísicas expresamente diseñadas en esta Tesis Doctoral, de un esquema de control biológicamente plausible para la reducción de la dimensionalidad en el problema de la coordinación del gesto de la mano, durante el movimiento de agarre. Este esquema de control es lo que se define en la Tesis como Biblioteca de Gestos.(4) El aprendizaje que permite el establecimiento de los programas motores tras la percepción del objeto se lleva a cabo a través de una novedosa arquitectura neuronal multi red inspirada en la conectividad cortical entre áreas del córtex parietal posterior y córtex promotor que, tras una serie de etapas de aprendizaje, es capaz de generar movimientos de agarre correctos para un conjunto brazo mano robot antropomorfo cuando a éste sistema se le presentan objetos de distinta forma y tamaño, independientemente de su localización u orientación en el espacio. La Tesis presenta numerosos resultados referentes a la simulación de los modelos en distintas situaciones así como resultados relativos a la implantación de dichos modelos sobre una plataforma robótica antropomorfa orientada al agarre de objetos. Dichos resultados sustentan las hipótesis teóricas que fundamentan esta investigación y por otra parte muestran las capacidades de los modelos desarrollados para actuar como controladores de alto nivel en el guiado de tareas de agarre manipuladores robóticos humanoides.[ENG] Robotics has become into a traditional field in which research is made by engineers and scientist from different science disciplines such as mathematics, physics, medicine, neurosciences etc. It is evident that in the last years , robotics has evolve to be a multidisciplinary area getting closer and closer to everyday life of human beings such as in the cases of robotics applied to rehabilitation or surgery. It also has been established the use of robotics as a tool for the study of the Man and other biological systems or even to construct artificial anthropomorphic components such as, arms, sensors or cognitive – behavioural schemas able to substitute their biological counterparts in some situations. In the last years, it has been established within the robotics community, the idea about that the understanding of the nervous system of humans and monkeys has also a potential industrial or productive interest. The artificial intelligence industrial devices are more and more inspired in Biology. The brain operates in way very different to the way an actual robot actually operates. The mechanisms for information processing are vastly more complex and subtle in brain neural circuits than in the electronic circuits of the actual robots. The interactions within groups of neurons modify the properties of neural firing of these neurons in their interaction with sensory signals from the external world. An elemental learning such as avoiding behaviours with negative consequences, imply millions of neuronal events, including the reconfiguration and establishment of new neuronal connections. This is what is called ‘adaptability to environment’ of the biological systems. Neuro – Robotics constitutes an emergent and new field which represents, in its objectives, a huge challenge for science ad technology: the transference of fundamental principles of the neurobiology that drives the human behaviour to the diversity of disciplines of the engineering that constitute the Robotics (signal processing, robust and adaptive control, non linear systems, pattern recognition, mechatronics, etc…). If Robotics always has been a multidisciplinary field basically at the technological level, the need to push this field into major advances, requires a stronger interaction between the roboticians and scientist from another fields such as neurosciences, physiology or psychology. The ideas exposed above are the general reference frame in which the work of this PhD Thesis is developed. Concretely, it could be said that, major objectives of this PhD coincide with major objectives of two basic research projects funded by European Commission: BRITE-SYNERAGH (Systems neuroscience and engineering research for anthropomorphic grasping and handling, 1998-2001, BRE-2-CT980797) project and IST/FET-PALOMA (Progressive and adaptive learning for object manipulation: a biologically inspired multi-network architecture, 2001-2004, IST-2001-33073) project. The author of this PhD Thesis is ascribed to NeuroTechnology, Control and Robotics research group of the Universidad Politécnica de Cartagena. This research group and the author of this Thesis, have been intensively involved in the development of the two mentioned European projects.Universidad Politécnica de CartagenaPrograma de doctorado en Tecnologías Industriales. Subprograma Neurotecnología, Control y Robótic