Physics has two main ambitions: to predict and to understand. Indeed, physics aims for the prediction of all natural phenomena. Prediction entails modeling the correlation between an action, the input, and what is subsequently observed, the output.Understanding, on the other hand, involves developing insightful principles and models that can explain the widest possible varietyof correlations present in nature. Remarkably, advances in both prediction and understanding foster our physical intuition and, as a consequence, novel and powerful applications are discovered. Quantum mechanics is a very successful physical theory both in terms of its predictive power as well as in its wide applicability. Nonetheless and despite many decades of development, we do not yet have a proper physical intuition of quantum phenomena. I believe that improvements in our understanding of quantum theory will yield better, and more innovative, protocols and vice versa.This dissertation aims at advancing our understanding and developing novel protocols. This is done through four approaches. The first one is to study quantum theory within a broad family of theories. In particular, we study quantum theory within the family of locally quantum theories. We found out that the principle that singles out quantum theory out of this family, thus connecting quantum local and nonlocal structure, is dynamical reversibility. This implies that the viability of large scale quantum computing can be based on concrete physical principles that can be experimentally tested at a local level without needing to test millions of qubits simultaneously. The second approach is to study quantum correlations from a black box perspective thus making as few assumptions as possible. The strategy is to study the completeness of quantum predictions by benchmarking them against alternative models. Three main results and applications come out of our study. Firstly, we prove that performing complete amplification of randomness starting from a source of arbitrarily weak randomness - a task that is impossible with classical resources - is indeed possible via nonlocality. This establishes in our opinion the strongest evidence for a truly random event in nature so far. Secondly, we prove that there exist finite events where quantum theory gives predictions as complete as any no-signaling theory can give, showing that the completeness of quantum theory is not an asymptotic property. Finally, we prove that maximally nonlocal theories can never be maximally random while quantum theory can, showing a trade-off between the nonlocality of a theory and its randomness capabilities. We also prove that quantum theory is not unique in this respect. The third approach we follow is to study quantum correlations in scenarios where some parties have a restriction on the available quantum degrees of freedom. The future progress of semi-device-independent quantum information depends crucially on our ability to bound the strength of these correlations. Here we provide a full characterization via a complete hierarchy of sets that approximate the target set from the outside. Each set can be in turn characterized using standard numerical techniques. One application of our work is certifying multidimensional entanglement device-independently.The fourth approach is to confront quantum theory with computer science principles. In particular, we establish two interesting implications for quantum theory results of raising the Church-Turing thesis to the level of postulate. Firstly, we show how different preparations of the same mixed state, indistinguishable according to the quantum postulates, become distinguishable when prepared computably. Secondly, we identify a new loophole for Bell-like experiments: if some parties in a Bell-like experiment use private pseudorandomness to choose their measurement inputs, the computational resources of an eavesdropper have to be limited to observe a proper violation of non locality.
Physics has two main ambitions: to predict and to understand. Indeed, physics aims for the prediction of all natural phenomena. Prediction entails modeling the correlation between an action, the input, and what is subsequently observed, the output.Understanding, on the other hand, involves developing insightful principles and models that can explain the widest possible varietyof correlations present in nature. Remarkably, advances in both prediction and understanding foster our physical intuition and, as a consequence, novel and powerful applications are discovered. Quantum mechanics is a very successful physical theory both in terms of its predictive power as well as in its wide applicability. Nonetheless and despite many decades of development, we do not yet have a proper physical intuition of quantum phenomena. I believe that improvements in our understanding of quantum theory will yield better, and more innovative, protocols and vice versa.This dissertation aims at advancing our understanding and developing novel protocols. This is done through four approaches. The first one is to study quantum theory within a broad family of theories. In particular, we study quantum theory within the family of locally quantum theories. We found out that the principle that singles out quantum theory out of this family, thus connecting quantum local and nonlocal structure, is dynamical reversibility. This implies that the viability of large scale quantum computing can be based on concrete physical principles that can be experimentally tested at a local level without needing to test millions of qubits simultaneously. The second approach is to study quantum correlations from a black box perspective thus making as few assumptions as possible. The strategy is to study the completeness of quantum predictions by benchmarking them against alternative models. Three main results and applications come out of our study. Firstly, we prove that performing complete amplification of randomness starting from a source of arbitrarily weak randomness - a task that is impossible with classical resources - is indeed possible via nonlocality. This establishes in our opinion the strongest evidence for a truly random event in nature so far. Secondly, we prove that there exist finite events where quantum theory gives predictions as complete as any no-signaling theory can give, showing that the completeness of quantum theory is not an asymptotic property. Finally, we prove that maximally nonlocal theories can never be maximally random while quantum theory can, showing a trade-off between the nonlocality of a theory and its randomness capabilities. We also prove that quantum theory is not unique in this respect. The third approach we follow is to study quantum correlations in scenarios where some parties have a restriction on the available quantum degrees of freedom. The future progress of semi-device-independent quantum information depends crucially on our ability to bound the strength of these correlations. Here we provide a full characterization via a complete hierarchy of sets that approximate the target set from the outside. Each set can be in turn characterized using standard numerical techniques. One application of our work is certifying multidimensional entanglement device-independently.The fourth approach is to confront quantum theory with computer science principles. In particular, we establish two interesting implications for quantum theory results of raising the Church-Turing thesis to the level of postulate. Firstly, we show how different preparations of the same mixed state, indistinguishable according to the quantum postulates, become distinguishable when prepared computably. Secondly, we identify a new loophole for Bell-like experiments: if some parties in a Bell-like experiment use private pseudorandomness to choose their measurement inputs, the computational resources of an eavesdropper have to be limited to observe a proper violation of non locality.
Physics has two main ambitions: to predict and to understand. Indeed, physics aims for the prediction of all natural phenomena. Prediction entails modeling the correlation between an action, the input, and what is subsequently observed, the output.Understanding, on the other hand, involves developing insightful principles and models that can explain the widest possible varietyof correlations present in nature. Remarkably, advances in both prediction and understanding foster our physical intuition and, as a consequence, novel and powerful applications are discovered. Quantum mechanics is a very successful physical theory both in terms of its predictive power as well as in its wide applicability. Nonetheless and despite many decades of development, we do not yet have a proper physical intuition of quantum phenomena. I believe that improvements in our understanding of quantum theory will yield better, and more innovative, protocols and vice versa.This dissertation aims at advancing our understanding and developing novel protocols. This is done through four approaches. The first one is to study quantum theory within a broad family of theories. In particular, we study quantum theory within the family of locally quantum theories. We found out that the principle that singles out quantum theory out of this family, thus connecting quantum local and nonlocal structure, is dynamical reversibility. This implies that the viability of large scale quantum computing can be based on concrete physical principles that can be experimentally tested at a local level without needing to test millions of qubits simultaneously. The second approach is to study quantum correlations from a black box perspective thus making as few assumptions as possible. The strategy is to study the completeness of quantum predictions by benchmarking them against alternative models. Three main results and applications come out of our study. Firstly, we prove that performing complete amplification of randomness starting from a source of arbitrarily weak randomness - a task that is impossible with classical resources - is indeed possible via nonlocality. This establishes in our opinion the strongest evidence for a truly random event in nature so far. Secondly, we prove that there exist finite events where quantum theory gives predictions as complete as any no-signaling theory can give, showing that the completeness of quantum theory is not an asymptotic property. Finally, we prove that maximally nonlocal theories can never be maximally random while quantum theory can, showing a trade-off between the nonlocality of a theory and its randomness capabilities. We also prove that quantum theory is not unique in this respect. The third approach we follow is to study quantum correlations in scenarios where some parties have a restriction on the available quantum degrees of freedom. The future progress of semi-device-independent quantum information depends crucially on our ability to bound the strength of these correlations. Here we provide a full characterization via a complete hierarchy of sets that approximate the target set from the outside. Each set can be in turn characterized using standard numerical techniques. One application of our work is certifying multidimensional entanglement device-independently.The fourth approach is to confront quantum theory with computer science principles. In particular, we establish two interesting implications for quantum theory results of raising the Church-Turing thesis to the level of postulate. Firstly, we show how different preparations of the same mixed state, indistinguishable according to the quantum postulates, become distinguishable when prepared computably. Secondly, we identify a new loophole for Bell-like experiments: if some parties in a Bell-like experiment use private pseudorandomness to choose their measurement inputs, the computational resources of an eavesdropper have to be limited to observe a proper violation of non locality. La física tiene dos finalidades: predecir y comprender. En efecto, la física aspira a poder predecir todos los fenómenos naturales. Predecir implica modelar correlaciones entre una acción y la reacción subsiguiente.Comprender, implica desarrollar leyes profundas que expliquen la más amplia gama de correlaciones presentes en la naturaleza. Avances tanto en la capacidad de predicción como en nuestra comprensión fomentan la intuición física y, como consecuencia, surgen nuevas y poderosas aplicaciones. La mecánica cuántica es una teoría física de enorme éxito por su capacidad de predicción y amplia aplicabilidad.Sin embargo, a pesar de décadas de gran desarrollo, no poseemos una intuición física satisfactoria de los fenómenos cuánticos.Creo que mejoras en nuestra comprensión de la teoría cuántica traerán consigo mejores y más innovadores protocolos y vice versa.Ésta tesis doctoral trata simultáneamente de avanzar nuestra comprensión y de desarrollar nuevos protocolos mediante cuatro enfoques distintos.El primero consiste en estudiar la mecánica cuántica como miembro de una familia de teorías: las teorías localmente cuánticas. Probamos que el principio que selecciona a la mecánica cuántica, conectando por tanto la estructura cuántica local y no local, es la reversibilidad de su dinámica.Ésto implica que la viabilidad de la computación cuántica a gran escala puede ser estudiada de manera local, comprobando experimentalmente ciertos principios físicos. El segundo enfoque consiste en estudiar las correlaciones cuánticas desde una perspectiva de 'caja negra', haciendo así el mínimo de asunciones físicas. La estrategia consiste en estudiar la completitud de las predicciones cuánticas, comparándolas con todos los modelos alternativos. Hemos obtenido tres grandes resultados. Primero, probamos que se puede amplificar completamente la aleatoriedad de una fuente de aleatoriedad arbitrariamente débil.Ésta tarea, imposible mediante recursos puramente clásicos, se vuelve factible gracias a la no localidad. Ésto establece a nuestro parecer la evidencia más fuerte de la existencia de eventos totalmente impredecibles en la naturaleza. Segundo, probamos que existen eventos finitos cuyas predicciones cuánticas son tan completas como permite el principio de 'no signaling'. Ésto prueba que la completitud de la mecánica cuántica no es una propiedad asintótica. Finalmente, probamos que las teorías máximamente no locales no pueden ser máximamente aleatorias, mientras que la mecánica cuántica lo es. Ésto muestra que hay una compensación entre la no localidad de una teoría y su capacidad para generar aleatoriedad. También probamos que la mecánica cuántica no es única en éste respecto. En tercer lugar, estudiamos las correlaciones cuánticas en escenarios dónde algunas partes tienen restricciones en el número de grados de libertad cuánticos accesibles. Éste escenario se denomina 'semi-device-independent'. Aquí encontramos una caracterización completa de éstas correlaciones mediante una jerarquía de conjuntos que aproximan al conjunto buscado desde fuera y que pueden ser caracterizados a su vez mediante técnicas numéricas estandar. Un aplicación de nuestro trabajo es la certificación de entrelazamiento multidimensional de manera 'device-independent'. El cuarto y último enfoque consiste en enfrentar a la mecánica cuántica con principios provenientes de la computación. En particular, establecemos dos implicaciones para la mecánica cuántica de elevar la tesis de Church-Turing al nivel de postulado. Primero, mostramos que diferentes preparaciones de un mismo estado mixto, indistinguibles de acuerdo a los axiomas cuánticos, devienen distinguibles cuando son preparados de manera computable. Segundo, identificamos un nuevo 'loophole' en experimentos de Bell: si algunas partes en un experimento de Bell usan pseudo aleatoriedad para escoger sus medidas, los recursos computacionales de un espía deben ser limitados a fin de observar verdaderamente la no localidad.
Despite the success of quantum mechanics in predicting the outcomes of experiments in many branches of physics, the foundations of the theory have remained subject of research and dispute. At the basis of this struggle with the theory lie the phenomena of nonlocality and entanglement. Since it was first predicted by Bell in 1964, nonlocality was not only verified in numerous experiments, but also identified as a useful resource for quantum information processing. Thus, the study of nonlocality is important both from a fundamental point of view and with respect to new applications in quantum information theory, such as secure cryptography and randomness generation. The identification of entanglement as a resource for quantum information led to a strong theoretical effort devoted to its characterisation and detection. Many of the resulting mathematical tools find application in several domains of physics. Although the only known way to create nonlocal correlations is to measure entangled quantum systems, it has been shown that entanglement and nonlocality constitute two inequivalent properties. Therefore, in the light of the success of entanglement theory, it is of interest to also devise a resource theory of nonlocality. The task of this thesis is to develop such a theoretical framework for the characterisation of nonlocality as a resource. To gain a better understanding of nonlocal correlations it will be necessary to investigate correlation scenarios that go beyond the situation originally considered by Bell. In doing so, this thesis provides new description of nonlocality that also have implications for the characterisation of quantum correlations and the detection of new forms of nonlocality. The first question we address is how nonlocality can consistently be defined in a scenario of arbitrarily many parties that may collaborate among each other. To this end we recognise which are the allowed physical operations in this situation and then define nonlocality as the resource that cannot be created by these operations. Our approach shows that the conventional definition of multipartite nonlocality, adopted by the community so far, is inconsistent with this operational definition; we further propose and analyse new models that do not suffer from these inconsistencies. Furthermore, we show that our findings have implications for the characterisation of quantum correlations. A recent approach to describe the set of quantum correlation consists in using principles inspired from information theory. By using a special instance of the models we defined earlier we show a fundamental limitation of this approach: no bipartite information principle is sufficient to single out the set of quantum correlations from the set of nonsignalling correlations. We then developed a description of nonlocality in an even more generalised scenario of several parties. Motivated by a result of Popescu we study scenarios where the parties are allowed to perform not only a single but sequences of measurements on their systems. Characterising nonlocality also in this scenario in operational terms and defining local models compatible with this definition, we show that a new form of nonlocality can be detected Lastly, we examine the problem of detecting the presence of nonlocality in a multipartite scenario when one is given only partial access to the global system. We find that one can verify that the total system must display nonlocality, even though the accessible subsystems only exhibit local correlations.
In the past century, experimental discoveries have witnessed phenomena in Nature which challenge our everyday classical intuition. In order to explain these facts, quantum theory was developed, which so far has been able to reproduce the observed results. However, I believe that our understanding of quantum mechanics can be significantly improved by the search for an operational meaning behind its mathematical formulation, which would help to identify the limitations and possibilities of the theory for information processing. An intriguing property of quantum theory is its intrinsic randomness. Indeed, Einstein, Podolsky and Rosen in 1935 questioned the completeness of quantum theory. They argued the possibility of the existence of a complete theory where variables to which we have not access determine the behaviour of physical systems, and the randomness observed in quantum mechanics is then due to our ignorance of these variables. These hidden variables theories, however, were proved not to be enough for explaining the predictions of quantum theory, as shown in the no-go theorems by Bell on quantum-nonlocality and by Kochen and Specker on quantum-contextuality. In the past decades, many experiments have corroborated the nonlocal and contextual character of Nature. However, no intuition behind these phenomena has been found, in particular about what limits their strength. In fact, special relativity alone would allow for phenomena which are more nonlocal than what quantum theory allows. Hence, much effort has been devoted to find the physical properties of quantum theory that restricts these phenomena. In this thesis, we study the constraints that arise on nonlocal and contextual phenomena when a certain exclusiveness structure compatible with quantum theory is imposed in the space of events. Here, an event denotes the situation where an outcome is obtained given that a measurement is performed on the physical system. Regarding nonlocality, we introduce a notion of orthogonality that states that events involving different outcomes of the same local measurement are exclusive, and construct constraints that the correlations among observers should satisfy. We denote this by Local Orthogonality principle (LO), which is the first intrinsically multipartite principle for bounding quantum correlations. We prove that LO identifies the supra-quantum character of some bipartite and multipartite correlations, and gets close to the quantum boundary. When studying contextuality, the same abstract event may correspond to outcomes of different measurements, which introduces a non-trivial structure in the space of events. For its study, we develop a general formalism for contextuality scenarios in the spirit of the recent approach by Cabello, Severini and Winter. In our framework, nonlocality arises as a particular case of contextuality, which allows us to study a generalization of LO. Both in nonlocality and contextuality, we find close connections to problems in combinatorics and hence use graph-theoretical tools for studying correlations. Finally, this thesis also studies the detection of nonlocal correlations. Most results on quantum nonlocality focus on few particles' experiments, while less is known about the detection of quantum nonlocality in many-body systems. Standard many-body observables involve correlations among few particles, while there is still no multipartite Bell inequality to test nonlocality merely from these data. In this thesis, we provide the first proposal for nonlocality detection in many-body systems using two-body correlations. We construct families of Bell inequalities from two-body correlators, which can detect nonlocality for systems with large number of constituents. In addition, we prove violations by systems which are relevant in nuclear and atomic physics, and show how to test these inequalities by measuring global spin components, hence opening the problem to experimental realizations.
Quantum mechanics was developed as a response to the inadequacy of classical physics in explaining certain physical phenomena. While it has proved immensely successful, it also presents several features that severely challenge our classicality based intuition. Randomness in quantum theory is one such and is the central theme of this dissertation. Randomness is a notion we have an intuitive grasp on since it appears to abound in nature. It a icts weather systems and nancial markets and is explicitly used in sport and gambling. It is used in a wide range of scienti c applications such as the simulation of genetic drift, population dynamics and molecular motion in fluids. Randomness (or the lack of it) is also central to philosophical concerns such as the existence of free will and anthropocentric notions of ethics and morality. The conception of randomness has evolved dramatically along with physical theory. While all randomness in classical theory can be fully attributed to a lack of knowledge of the observer, quantum theory qualitatively departs by allowing the existence of objective or intrinsic randomness. It is now known that intrinsic randomness is a generic feature of hypothetical theories larger than quantum theory called the non-signalling theories. They are usually studied with regards to a potential future completion of quantum mechanics or from the perspective of recognizing new physical principles describing nature. While several aspects have been studied to date, there has been little work in globally characterizing and quantifying randomness in quantum and non-signalling theories and the relationship between them. This dissertation is an attempt to ll this gap. Beginning with the unavoidable assumption of a weak source of randomness in the universe, we characterize upper bounds on quantum and non-signalling randomness. We develop a simple symmetry argument that helps identify maximal randomness in quantum theory and demonstrate its use in several explicit examples. Furthermore, we show that maximal randomness is forbidden within general non-signalling theories and constitutes a quantitative departure from quantum theory. We next address (what was) an open question about randomness ampli cation. It is known that a single source of randomness cannot be ampli ed using classical resources alone. We show that using quantum resources on the other hand allows a full ampli cation of the weakest sources of randomness to maximal randomness even in the presence of supra-quantum adversaries. The signi cance of this result spans practical cryptographic scenarios as well as foundational concerns. It demonstrates that conditional on the smallest set of assumptions, the existence of the weakest randomness in the universe guarantees the existence of maximal randomness. The next question we address is the quanti cation of intrinsic randomness in non-signalling correlations. While this is intractable in general, we identify cases where this can be quanti ed. We nd that in these cases all observed randomness is intrinsic even relaxing the measurement independence assumption. We nally turn to the study of the only known resource that allows generating certi able intrinsic randomness in the laboratory i.e. entanglement. We address noisy quantum systems and calculate their entanglement dynamics under decoherence. We identify exact results for several realistic noise models and provide tight bounds in some other cases. We conclude by putting our results into perspective, pointing out some drawbacks and future avenues of work in addressing these concerns.
Quantum mechanics has been a paradigm shift and a revolutionary framework in our understanding of the physical world. The theory has been able to describe a wide variety of phenomena and has been experimentally verified with great precision. Despite that, to this day, the seemingly ad hoc formulation of quantum theory and several of its features still elude an intuitive understanding. At the same time, the applications of quantum mechanics in information theory have emerged as a promising avenue. Namely, its potential advantages in computation, in the so-called nascent field of quantum computation and in communication and information processing tasks such as quantum teleportation and super-dense coding. In all these endeavours, a significant effort has been made in understanding the maximum extent to which quantum mechanics can provide an advantage. This thesis explores an intersection of these two research lines, i.e. to have a physical explanation of some of the features of quantum mechanics and at the same time, study the outer limits of quantum mechanics. The combining insight rests on a newer foundational idea: that information itself is physical rather than an abstract entity and thus, is subject to physical laws. In this thesis, we explore the principle of information causality, which states that in any communication scenario, the amount of information carried is bounded by the degrees of freedom of the carrier. Information causality was initially proposed as a physical principle aimed at deriving the predictions of quantum mechanics on the type of correlations observed in a Bell scenario, which is a communication scenario involving multiple parties with access to a shared randomness resource. This principle has been proposed to recover some of the well-known features of quantum mechanics, specifically Tsirelson’s bound of the Clauser-Horne-Shimony-Holt inequality. Earlier results found limited generalisations due to the difficulty of deducing implications of the information causality principle. In this thesis, we greatly expand the scope of applicability of the principle. We develop a general-purpose algorithm to derive constraints on the set of quantum correlations. We extend the principle to be applicable to a wider variety of Bell scenarios, derive new families of quantum Bell inequalities and prove new bounds on the success probabilities of Entanglement Assisted Random Access Codes. We introduce an extension of the principle which applies to any distributed computing scenario. Using this extension, we improve on several previously known results in the field, and in certain cases, we even recover part of the quantum set as well. This extension provides rich insights into the communication complexity of distributed functions, using which we prove theory-independent randomised communication complexity bounds for several well-known functions and provide another general-purpose algorithm to bound the randomised quantum communication complexity of any function. As a consequence of the extension, we also establish that the extension supersedes the principle of non-trivial communication complexity.
Quantum physics provides results at information processing tasks that are unattainable by any classical theory. The aim of this thesis is to identify and characterize quantum entanglement and quantum nonlocality, the key resources used at quantum information protocols. We consider the problem of finding better experimental schemes to detect entangled states. For that, we study approximate physical realizations to non-physical processes, which provide the most efficient method to identify entanglement. We prove that many of these physical approximations have a simple experimental implementation. We then study characterization of quantum nonlocality. We introduce a method using the multipartite scenario, where more than two parties are involved, which provides several results on bipartite and multipartite quantum nonlocality. First, we prove that there exist quantum states which contain full multipartite nonlocality, which consist of the strongest kind of nonlocality. then, we prove that the combined use of several copies of a state can activate its nonlocal properties. In particular, this holds for bipartite and genuine multipartite nonlocality. Finally, we characterize quantum nonlocality by distinguishing it from stronger-than-quantum nonlocality. We construct a multipartite game for which classical and quantum players perform equally well, but for which supre-quantum players can sometimes provide an advantage. Our results suggest that physical resources might obbey a generalized no-signaling principle ( according to which ther's no instantaneous communication).