The classical-quantum boundary for correlations: discord and related measures

One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more actively-studied topics of quantum information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here we review different notions of classical and quantum correlations quantified by quantum discord and other related measures. In the first half, we review the mathematical properties of the measures of quantum correlations, relate them to each other, and discuss the classical-quantum division that is common among them. In the second half, we show that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. We show that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.Comment: Close to the published versio

Quantum information outside quantum information

Premi Extraordinari de Doctorat, promoció 2018-2019. Àmbit de CiènciesQuantum theory, as counter-intuitive as a theory can get, has turned out to make predictions of the physical world that match observations so precisely that it has been described as the most accurate physical theory ever devised. Viewing quantum entanglement, superposition and interference not as undesirable necessities but as interesting resources paved the way to the development of quantum information science. This area studies the processing, transmission and storage of information when one accounts that information is physical and subjected to the laws of nature that govern the systems it is encoded in. The development of the consequences of this idea, along with the great advances experienced in the control of individual quantum systems, has led to what is now known as the second quantum revolution, in which quantum information science has emerged as a fully-grown field. As such, ideas and tools developed within the framework of quantum information theory begin to permeate to other fields of research. This Ph.D. dissertation is devoted to the use of concepts and methods akin to the field of quantum information science in other areas of research. In the same way, it also considers how encoding information in quantum degrees of freedom may allow further development of well-established research fields and industries. This is, this thesis aims to the study of quantum information outside the field of quantum information. Four different areas are visited. A first question posed is that of the role of quantum information in quantum field theory, with a focus in the quantum vacuum. It is known that the quantum vacuum contains entanglement, but it remains unknown whether it can be accessed and exploited in experiments. We give crucial steps in this direction by studying the extraction of vacuum entanglement in realistic models of light-matter interaction, and by giving strict mathematical conditions of general applicability that must be fulfilled for extraction to be possible at all. Another field where quantum information methods can offer great insight is in that of quantum thermodynamics, where the idealizations made in macroscopic thermodynamics break down. Making use of a quintessential framework of quantum information and quantum optics, we study the cyclic operation of a microscopic heat engine composed by a single particle reciprocating between two finite-size baths, focusing on the consequences of the removal of the macroscopic idealizations. One more step down the stairs to applications in society, we analyze the impact that encoding information in quantum systems and processing it in quantum computers may have in the field of machine learning. A great desideratum in this area, largely obstructed by computational power, is that of explainable models which not only make predictions but also provide information about the decision process that triggers them. We develop an algorithm to train neural networks using explainable techniques that exploits entanglement and superposition to execute efficiently in quantum computers, in contrast with classical counterparts. Furthermore, we run it in state-of-the-art quantum computers with the aim of assessing the viability of realistic implementations. Lastly, and encompassing all the above, we explore the notion of causality in quantum mechanics from an information-theoretic point of view. While it is known since the work of John S. Bell in 1964 that, for a same causal pattern, quantum systems can generate correlations between variables that are impossible to obtain employing only classical systems, there is an important lack of tools to study complex causal effects whenever a quantum behavior is expected. We fill this gap by providing general methods for the characterization of the quantum correlations achievable in complex causal patterns. Closing the circle, we make use of these tools to find phenomena of fundamental and experimental relevance back in quantum information.La teoría cuántica, la más extraña y antiintuitiva de las teorías físicas, es también considerada como la teoría más precisa jamás desarrollada. La interpretación del entrelazamiento, la superposición y la interferencia como interesantes recursos aprovechables cimentó el desarrollo de la teoría cuántica de la información (QIT), que estudia el procesado, transmisión y almacenamiento de información teniendo en cuenta que ésta es física, en tanto a que está sujeta a las leyes de la naturaleza que gobiernan los sistemas en que se codifica. El desarrollo de esta idea, en conjunción con los recientes avances en el control de sistemas cuánticos individuales, ha dado lugar a la conocida como segunda revolución cuántica, en la cual la QIT ha emergido como un área de estudio con denominación propia. A consecuencia de su desarrollo actual, ideas y herramientas creadas en su seno comienzan a permear a otros ámbitos de investigación. Esta tesis doctoral está dedicada a la utilización de conceptos y métodos originales del campo de información cuántica en otras áreas. También considera cómo la codificación de información en grados de libertad cuánticos puede afectar el futuro desarrollo de áreas de investigación e industrias bien establecidas. Es decir, esta tesis tiene como objetivo el estudio de la información cuántica fuera de la información cuántica, haciendo hincapié en cuatro ámbitos diferentes. Una primera cuestión propuesta es la del papel de la información cuántica en la teoría cuántica de campos, con especial énfasis en el vacío cuántico. Es conocido que el vacío cuántico contiene entrelazamiento, pero aún se desconoce éste es accesible para su uso en realizaciones experimentales. En esta tesis se dan pasos cruciales en esta dirección mediante el estudio de la extracción de entrelazamiento en modelos realistas de la interacción materia-radiación, y dando condiciones matemáticas estrictas que deben ser satisfechas para que dicha extracción sea posible. Otro campo en el cual métodos propios de QIT pueden ofrecer nuevos puntos de vista es en termodinámica cuántica. A través del uso de un marco de trabajo ampliamente utilizado en información y óptica cuánticas, estudiamos la operación cíclica de un motor térmico microscópico que alterna entre dos baños térmicos de tamaño finito, prestando especial atención a las consecuencias de la eliminación de las idealizaciones macroscópicas utilizadas en termodinámica macroscópica. Acercándonos a aplicaciones industriales, analizamos el potencial impacto de codificar y procesar información en sistemas cuánticos en el ámbito del aprendizaje automático. Un fin codiciado en esta área, inaccesible debido a su coste computacional, es el de modelos explicativos que realicen predicciones, y además ofrezcan información acerca del proceso de decisión que las genera. Presentamos un algoritmo de entrenamiento de redes neuronales con técnicas explicativas que hace uso del entrelazamiento y la superposición para tener una ejecución eficiente en ordenadores cuánticos, en comparación con homólogos clásicos. Además, ejecutamos el algoritmo en ordenadores cuánticos contemporáneos con el objetivo de evaluar la viabilidad de implementaciones realistas. Finalmente, y englobando todo lo anterior, exploramos la noción de causalidad en mecánica cuántica desde el punto de vista de la teoría de la información. A pesar de que es conocido que para un mismo patrón causal existen sistemas cuánticos que dan lugar a correlaciones imposibles de generar por mediación de sistemas clásicos, existe una notable falta de herramientas para estudiar efectos causales cuánticos complejos. Cubrimos esta falta mediante métodos generales para la caracterización de las correlaciones cuánticas que pueden ser generadas en estructuras causales complejas. Cerrando el círculo, usamos estas herramientas para encontrar fenómenos de relevancia fundamental y experimental en la información cuánticaPostprint (published version

Quantum information outside quantum information

Quantum theory, as counter-intuitive as a theory can get, has turned out to make predictions of the physical world that match observations so precisely that it has been described as the most accurate physical theory ever devised. Viewing quantum entanglement, superposition and interference not as undesirable necessities but as interesting resources paved the way to the development of quantum information science. This area studies the processing, transmission and storage of information when one accounts that information is physical and subjected to the laws of nature that govern the systems it is encoded in. The development of the consequences of this idea, along with the great advances experienced in the control of individual quantum systems, has led to what is now known as the second quantum revolution, in which quantum information science has emerged as a fully-grown field. As such, ideas and tools developed within the framework of quantum information theory begin to permeate to other fields of research. This Ph.D. dissertation is devoted to the use of concepts and methods akin to the field of quantum information science in other areas of research. In the same way, it also considers how encoding information in quantum degrees of freedom may allow further development of well-established research fields and industries. This is, this thesis aims to the study of quantum information outside the field of quantum information. Four different areas are visited. A first question posed is that of the role of quantum information in quantum field theory, with a focus in the quantum vacuum. It is known that the quantum vacuum contains entanglement, but it remains unknown whether it can be accessed and exploited in experiments. We give crucial steps in this direction by studying the extraction of vacuum entanglement in realistic models of light-matter interaction, and by giving strict mathematical conditions of general applicability that must be fulfilled for extraction to be possible at all. Another field where quantum information methods can offer great insight is in that of quantum thermodynamics, where the idealizations made in macroscopic thermodynamics break down. Making use of a quintessential framework of quantum information and quantum optics, we study the cyclic operation of a microscopic heat engine composed by a single particle reciprocating between two finite-size baths, focusing on the consequences of the removal of the macroscopic idealizations. One more step down the stairs to applications in society, we analyze the impact that encoding information in quantum systems and processing it in quantum computers may have in the field of machine learning. A great desideratum in this area, largely obstructed by computational power, is that of explainable models which not only make predictions but also provide information about the decision process that triggers them. We develop an algorithm to train neural networks using explainable techniques that exploits entanglement and superposition to execute efficiently in quantum computers, in contrast with classical counterparts. Furthermore, we run it in state-of-the-art quantum computers with the aim of assessing the viability of realistic implementations. Lastly, and encompassing all the above, we explore the notion of causality in quantum mechanics from an information-theoretic point of view. While it is known since the work of John S. Bell in 1964 that, for a same causal pattern, quantum systems can generate correlations between variables that are impossible to obtain employing only classical systems, there is an important lack of tools to study complex causal effects whenever a quantum behavior is expected. We fill this gap by providing general methods for the characterization of the quantum correlations achievable in complex causal patterns. Closing the circle, we make use of these tools to find phenomena of fundamental and experimental relevance back in quantum information.La teoría cuántica, la más extraña y antiintuitiva de las teorías físicas, es también considerada como la teoría más precisa jamás desarrollada. La interpretación del entrelazamiento, la superposición y la interferencia como interesantes recursos aprovechables cimentó el desarrollo de la teoría cuántica de la información (QIT), que estudia el procesado, transmisión y almacenamiento de información teniendo en cuenta que ésta es física, en tanto a que está sujeta a las leyes de la naturaleza que gobiernan los sistemas en que se codifica. El desarrollo de esta idea, en conjunción con los recientes avances en el control de sistemas cuánticos individuales, ha dado lugar a la conocida como segunda revolución cuántica, en la cual la QIT ha emergido como un área de estudio con denominación propia. A consecuencia de su desarrollo actual, ideas y herramientas creadas en su seno comienzan a permear a otros ámbitos de investigación. Esta tesis doctoral está dedicada a la utilización de conceptos y métodos originales del campo de información cuántica en otras áreas. También considera cómo la codificación de información en grados de libertad cuánticos puede afectar el futuro desarrollo de áreas de investigación e industrias bien establecidas. Es decir, esta tesis tiene como objetivo el estudio de la información cuántica fuera de la información cuántica, haciendo hincapié en cuatro ámbitos diferentes. Una primera cuestión propuesta es la del papel de la información cuántica en la teoría cuántica de campos, con especial énfasis en el vacío cuántico. Es conocido que el vacío cuántico contiene entrelazamiento, pero aún se desconoce éste es accesible para su uso en realizaciones experimentales. En esta tesis se dan pasos cruciales en esta dirección mediante el estudio de la extracción de entrelazamiento en modelos realistas de la interacción materia-radiación, y dando condiciones matemáticas estrictas que deben ser satisfechas para que dicha extracción sea posible. Otro campo en el cual métodos propios de QIT pueden ofrecer nuevos puntos de vista es en termodinámica cuántica. A través del uso de un marco de trabajo ampliamente utilizado en información y óptica cuánticas, estudiamos la operación cíclica de un motor térmico microscópico que alterna entre dos baños térmicos de tamaño finito, prestando especial atención a las consecuencias de la eliminación de las idealizaciones macroscópicas utilizadas en termodinámica macroscópica. Acercándonos a aplicaciones industriales, analizamos el potencial impacto de codificar y procesar información en sistemas cuánticos en el ámbito del aprendizaje automático. Un fin codiciado en esta área, inaccesible debido a su coste computacional, es el de modelos explicativos que realicen predicciones, y además ofrezcan información acerca del proceso de decisión que las genera. Presentamos un algoritmo de entrenamiento de redes neuronales con técnicas explicativas que hace uso del entrelazamiento y la superposición para tener una ejecución eficiente en ordenadores cuánticos, en comparación con homólogos clásicos. Además, ejecutamos el algoritmo en ordenadores cuánticos contemporáneos con el objetivo de evaluar la viabilidad de implementaciones realistas. Finalmente, y englobando todo lo anterior, exploramos la noción de causalidad en mecánica cuántica desde el punto de vista de la teoría de la información. A pesar de que es conocido que para un mismo patrón causal existen sistemas cuánticos que dan lugar a correlaciones imposibles de generar por mediación de sistemas clásicos, existe una notable falta de herramientas para estudiar efectos causales cuánticos complejos. Cubrimos esta falta mediante métodos generales para la caracterización de las correlaciones cuánticas que pueden ser generadas en estructuras causales complejas. Cerrando el círculo, usamos estas herramientas para encontrar fenómenos de relevancia fundamental y experimental en la información cuántic

Nonlocal correlations between freely propagating pairs of atoms

Since the formulation of quantum theory in the early twentieth century, its counterintuitive description of nature has shifted dramatically from being considered its weakness, to opening up vibrant fields of research and enabling classically untenable technologies. Perhaps the most striking aspect of quantum mechanics is exhibited in the infamous Einstein-Podolsky-Rosen (EPR) paradox, as the violation of locality from distant entangled particles. Due to many stringent technical requirements in the test of quantum nonlocality however, experimentalists have only recently demonstrated the nonlocal nature of quantum mechanics. Such well-controlled physical systems were few just a decade ago. This thesis contributes to the exponentially growing diversity of physical systems exhibiting quantum nonlocality, specifically between freely propagating massive particles, realised from an elastic collision of two helium atoms. This work investigates the entanglement between internal states of the scattered atom pairs, which opens up many exciting avenues to studying entanglement in motional variables of massive particles as well, since both types of entanglement are prepared in a collision. The thesis is composed of three projects, starting with an upgrade to the existing experimental apparatus to more stably produce ultracold gases of metastable helium. Massive particles such as atoms exhibit a wave-like behaviour at ultracold temperatures, typically requiring micro-Kelvin temperatures for a dilute gas. Laser cooling and trapping techniques in ultrahigh vacuum chambers are the workhorse of achieving such temperatures in atomic gases. The master laser system for the experimental apparatus was designed on an external-cavity diode laser, and is central to preparing Bose-Einstein condensates (BEC) of the dilute gas of metastable helium. BECs exhibit coherence in interference experiments which earn the term macroscopic matter-waves. As such, replicating classical optics phenomena with matterwaves has been of great interest since the first experimental realisation and manipulation of BECs. Here we study quantum correlations arising from a collision of BECs. In the particle picture counter-propagating pairs of atoms scatter, and quantum mechanically these pairs are expected to be entangled in their momentum and spin from conservation rules. The spins of spatially separate pairs are experimentally verified to be entangled, and exhibit EPR's "spooky" nonlocal correlations. Finally, we demonstrate the spatially separated entanglement in the freely propagating pairs of atoms in an application to quantum sensing. In this task the magnetic field gradient along the pairs' trajectories causes the atomic pair's correlation to oscillate. The pairwise entanglement enables the measurement to decouple from a common noise source, such as spatial uniform fluctuations in the magnetic field, and surpass the classical limit of measurement sensitivity

Control and Verification of Quantum Mechanical Systems

Quantum information science uses the distinguishing features of quantum mechanics for novel information processing tasks, ranging from metrology to computation. This manuscript explores multiple topics in this field. We discuss implementations of hybrid quantum systems composed of trapped ions and superconducting circuits, protocols for detecting signatures of entanglement in small and many-body systems, and a proposal for ground state preparation in quantum Hamiltonian simulators

Fault-tolerance in two-dimensional topological systems

This thesis is a collection of ideas with the general goal of building, at least in the abstract, a local fault-tolerant quantum computer. The connection between quantum information and topology has proven to be an active area of research in several fields. The introduction of the toric code by Alexei Kitaev demonstrated the usefulness of topology for quantum memory and quantum computation. Many quantum codes used for quantum memory are modeled by spin systems on a lattice, with operators that extract syndrome information placed on vertices or faces of the lattice. It is natural to wonder whether the useful codes in such systems can be classified. This thesis presents work that leverages ideas from topology and graph theory to explore the space of such codes. Homological stabilizer codes are introduced and it is shown that, under a set of reasonable assumptions, any qubit homological stabilizer code is equivalent to either a toric code or a color code. Additionally, the toric code and the color code correspond to distinct classes of graphs. Many systems have been proposed as candidate quantum computers. It is very desirable to design quantum computing architectures with two-dimensional layouts and low complexity in parity-checking circuitry. Kitaev\u27s surface codes provided the first example of codes satisfying this property. They provided a new route to fault tolerance with more modest overheads and thresholds approaching 1%. The recently discovered color codes share many properties with the surface codes, such as the ability to perform syndrome extraction locally in two dimensions. Some families of color codes admit a transversal implementation of the entire Clifford group. This work investigates color codes on the 4.8.8 lattice known as triangular codes. I develop a fault-tolerant error-correction strategy for these codes in which repeated syndrome measurements on this lattice generate a three-dimensional space-time combinatorial structure. I then develop an integer program that analyzes this structure and determines the most likely set of errors consistent with the observed syndrome values. I implement this integer program to find the threshold for depolarizing noise on small versions of these triangular codes. Because the threshold for magic-state distillation is likely to be higher than this value and because logical CNOT gates can be performed by code deformation in a single block instead of between pairs of blocks, the threshold for fault-tolerant quantum memory for these codes is also the threshold for fault-tolerant quantum computation with them. Since the advent of a threshold theorem for quantum computers much has been improved upon. Thresholds have increased, architectures have become more local, and gate sets have been simplified. The overhead for magic-state distillation has been studied, but not nearly to the extent of the aforementioned topics. A method for greatly reducing this overhead, known as reusable magic states, is studied here. While examples of reusable magic states exist for Clifford gates, I give strong reasons to believe they do not exist for non-Clifford gates

Nuclear-electronic spin systems, magnetic resonance, and quantum information processing

A promising platform for quantum information processing is that of silicon impurities, where the quantum states are manipulated by magnetic resonance. Such systems, in abstraction, can be considered as a nucleus of arbitrary spin coupled to an electron of spin one-half via an isotropic hyperfine interaction. We therefore refer to them as nuclear-electronic spin systems. The traditional example, being subject to intensive experimental studies, is that of phosphorus doped silicon (Si:P) which couples a spin one-half electron to a nucleus of the same spin, with a hyperfine strength of 117.5 MHz. More recently, bismuth doped silicon (Si:Bi) has been suggested as an alternative instantiation of nuclear-electronic spin systems, differing from Si:P by its larger nuclear spin and hyperfine strength of 9/2 and 1.4754 GHz respectively. The aim of this thesis has been to develop a model that is capable of predicting the magnetic resonance properties of nuclear-electronic spin systems. The theoretical predictions of this model have been tested against experimental data collected on Si:Bi at 4.044 GHz, and have proven quite successful. Furthermore, the larger nuclear spin and hyperfine strength of Si:Bi, compared with that of Si:P, are predicted to offer advantages for quantum information processing. Most notable amongst these is that magnetic field-dependent two-dimensional decoherence free subspaces, called optimal working points, have been identified to exist in Si:Bi, but not Si:P