Publication: Stability and area law for radpidly mixing quantum dissipative systems
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2017-05-24
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Universidad Complutense de Madrid
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Abstract
Desde su origen, la teoría de la información ha tenido fuertes conexiones con la mecánica estadística: el mismo término entropía de la información fue elegido por Shannon a partir del término usado en termodinámica, bajo sugerencia de Von Neumann [5, 67, 82]. Tradicionalmente la teoría de la información estudia el almacenamiento (códigos) y la transmisión a través de canales con ruido (capacidad de comunicación). Al interpretar las interacciones físicas como canales de comunicación, ha sido posible aplicar las mismas técnicas e ideas para entender cómo un sistema mecánico compuesto de muchas (o infinitas) partes desarrolla un comportamiento colectivo a partir de las interacciones simples y limitadas entre sus componentes individuales. Esto ha permitido entender el mecanismo con el cual propiedades macroscópicas aparecen como efectos de interacciones microscópicas. La misma relación se ha desarrollado recientemente entre las correspondientes generalizaciones cuánticas de ambas teorías: la información cuántica (que estudia el almacenamiento y la manipulación de la información en sistemas cuánticos) y la física de muchos cuerpos. Las conexiones entre los dos campos aumentan cada día y van en las dos direcciones: herramientas e ideas de la información cuántica ayudan a solucionar problemas abiertos en teoría de la materia condensada, y nuevos modelos de muchos cuerpos se desarrollan para aplicaciones de la información cuántica. Almismo tiempo la implementación y el control experimental de pequeños sistemas cuánticos ha mejorado de forma espectacular, aumentando la posibilidad de que estos experimentos se puedan llevar a cabo a escala más grande. Experimentos más grandes significa estar cada vezmás cerca de aplicaciones prácticas, lo cual ha orientado hacia el campo el interés de importantes universidades y centros de investigación, así como agencias nacionales de financiación como el EPSRC y la NSF, empresas privadas con fuerte inversión en la investigación y el desarrollo como IBM, Microsoft y Google...
Since its origins, the field of information theory has had strong ties to statistical mechanics: the terminology entropy of information was borrowed by Shannon from the thermodynamic entropy, as suggested by Von Neumann [5, 67, 82]. Traditionally information theory studies the storage of information (coding) and its transmission in noisy channels (communication capacity). By interpreting the physical interactions as communications channels, it has been possible to apply the same tools and ideas in order to understand how the collective behavior of a mechanical system composed of many (or infinite) parties emerges from the simple and limited interactions between its individual components. This has lead to understand the mechanism by which macroscopic properties emerge as effective behavior from microscopic interactions. The same relationship has been developed recently between the corresponding quantum generalizations of both theories: quantuminformation (which is interested in the storage and manipulation of information in quantummechanical systems) andmany-body quantumphysics. The ever-growing number of connections between the two fields goes in both directions, with tools and ideas fromquantuminformation helping to solve long-standing problems in condensed matter physics, and new many-body models being developed for the storage and the transformation of quantum information. At the same time the spectacular improvements we have seen in the implementation and experimental control of small quantumsystems is fueling the expectation that these experiments could be scaled up in size. Larger experiments means being closer to have practical applications, which has driven interest from top universities and research centers, national funding bodies such as EPSRC and NSF, to private companies with a strong focus on technological research as IBM, Microsoft and Google...
Since its origins, the field of information theory has had strong ties to statistical mechanics: the terminology entropy of information was borrowed by Shannon from the thermodynamic entropy, as suggested by Von Neumann [5, 67, 82]. Traditionally information theory studies the storage of information (coding) and its transmission in noisy channels (communication capacity). By interpreting the physical interactions as communications channels, it has been possible to apply the same tools and ideas in order to understand how the collective behavior of a mechanical system composed of many (or infinite) parties emerges from the simple and limited interactions between its individual components. This has lead to understand the mechanism by which macroscopic properties emerge as effective behavior from microscopic interactions. The same relationship has been developed recently between the corresponding quantum generalizations of both theories: quantuminformation (which is interested in the storage and manipulation of information in quantummechanical systems) andmany-body quantumphysics. The ever-growing number of connections between the two fields goes in both directions, with tools and ideas fromquantuminformation helping to solve long-standing problems in condensed matter physics, and new many-body models being developed for the storage and the transformation of quantum information. At the same time the spectacular improvements we have seen in the implementation and experimental control of small quantumsystems is fueling the expectation that these experiments could be scaled up in size. Larger experiments means being closer to have practical applications, which has driven interest from top universities and research centers, national funding bodies such as EPSRC and NSF, to private companies with a strong focus on technological research as IBM, Microsoft and Google...
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Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, Departamento de Análisis Matemático, leída el 07-07-2016