Quantum systems are able to show correlations between its parties that are stronger than correlations found in classical systems. Some of those strong correlations are called nonlocal, as for the classical correlations, they are calledlocal. Nonlocal correlations do not imply long-distance actions or superluminal communication, because they satisfy the nonsignaling condition. There are nonsignaling correlations stronger than quantum correlations because the quantum correlation set is a strictsubset of the nonsignaling correlation set. Quantum correlations are determined by how one obtains the probabilities of geting results conditioned to the measurement choices, considering the density operator describing the quantum state and the set of measurements. Moreover, a physical principle capable of justify quantum nonlocality is unkown. Because of that, an important question appeared:Would there be a physical principle which is able to explain the quantum nonlocality limits? Within the attempt to reach a positive answer for this question, some principles were presented in the last years. One of the most highlighted ones is the so-calledInformation Causality. This principle states that when one considers a system with two correlationedparties and the sending of a message from one party to the other containingd bits of information, the information gain within this process is limited tod bits. Quantum correlations satisfy the Information Causality principle. The best criteria known for the principle are able to discard most of the nonsignaling correlations that are stronger than quantum correlations, in the most simple scenarios. However, there still are supra-quantum correlations that obey such criteria. Recently, a new approach has been adopted for the achievement of a stronger criteriontorepresenttheInformationCausalityprinciple.Suchapproachisbasedonclassicaland quantum information theory, and causal inference theory, the latter being a powerful and interesting theory that relates the correlations with causal relations. This theory has found applications in many areas.This thesis presents the main elements of information theory, causal inference theory and nonlocality, aiming the analysis of the Information Causality principle and its strongest criterion. The main results obtained for the principle will be revised, and it will be presented a partial result obtained for a generalization of the more recent Information Causality criterion by considering scenarios in which multiple copies of the nonlocal resource are available.
Quantum systems are able to show correlations between its parties that are stronger than correlations found in classical systems. Some of those strong correlations are called nonlocal, as for the classical correlations, they are calledlocal. Nonlocal correlations do not imply long-distance actions or superluminal communication, because they satisfy the nonsignaling condition. There are nonsignaling correlations stronger than quantum correlations because the quantum correlation set is a strictsubset of the nonsignaling correlation set. Quantum correlations are determined by how one obtains the probabilities of geting results conditioned to the measurement choices, considering the density operator describing the quantum state and the set of measurements. Moreover, a physical principle capable of justify quantum nonlocality is unkown. Because of that, an important question appeared:Would there be a physical principle which is able to explain the quantum nonlocality limits? Within the attempt to reach a positive answer for this question, some principles were presented in the last years. One of the most highlighted ones is the so-calledInformation Causality. This principle states that when one considers a system with two correlationedparties and the sending of a message from one party to the other containingd bits of information, the information gain within this process is limited tod bits. Quantum correlations satisfy the Information Causality principle. The best criteria known for the principle are able to discard most of the nonsignaling correlations that are stronger than quantum correlations, in the most simple scenarios. However, there still are supra-quantum correlations that obey such criteria. Recently, a new approach has been adopted for the achievement of a stronger criteriontorepresenttheInformationCausalityprinciple.Suchapproachisbasedonclassicaland quantum information theory, and causal inference theory, the latter being a powerful and interesting theory that relates the correlations with causal relations. This theory has found applications in many areas.This thesis presents the main elements of information theory, causal inference theory and nonlocality, aiming the analysis of the Information Causality principle and its strongest criterion. The main results obtained for the principle will be revised, and it will be presented a partial result obtained for a generalization of the more recent Information Causality criterion by considering scenarios in which multiple copies of the nonlocal resource are available.
The Bell nonlocality is one of the most intriguing and counterintuitive phenomena displayed by quantum systems. Interestingly, such stronger-than-classical quantum correlations are somehow constrained, and one important question to the foundations of quantum theory is whether there is a physical, operational principle responsible for those constraints. One candidate is the information causality principle, which, in some particular cases, is proven to hold for quantum systems and to be violated by stronger-than-quantum correlations. In multipartite scenarios, though, it is known that the original formulation of the information causality principle fails to detect even extremal stronger-than-quantum correlations, thus suggesting that a genuinely multipartite formulation of the principle is necessary. In this work, we advance towards this goal, reporting a different formulation of the information causality principle in multipartite scenarios. By proposing a change of perspective, we obtain multipartite informational inequalities that work as necessary criteria for the principle to hold. We prove that such inequalities hold for all quantum resources and forbid some stronger-than-quantum ones. Finally, we show that our approach can be strengthened if multiple copies of the resource are available, or, counterintuitively, if noisy communication channels are employed.
Bell's theorem asserts that no local hidden variable theory can explain the predictions of quantum theory in an experiment where spacelike separated measurements are performed in distant laboratories. Loophole-free Bell tests performed in the last decade demonstrate Bell nonlocality as a property of Nature. However, the amount of nonlocality allowed in quantum theory is limited, compared to the sole restriction of no-signaling, meaning the impossibility of faster-than-light communication implied by special relativity. Information causality is a physical principle that generalizes no-signaling and is satisfied by quantum theory. It is based on the idea that shared quantum entanglement cannot enable a receiver to obtain more classical information than how much was sent by a distant sender. Remarkably, the principle was shown to imply the maximal quantum bound for the violation of the most well-known Bell inequality. The aim of this thesis is to widen our understanding of information causality and compare its predictions with other known outer approximations of the quantum set of correlations. We build upon the recent realization that most of the known consequences of information causality can be derived with a single copy of the shared systems, whereas before it was thought that many copies were necessary. We develop a novel optimization framework which bounds the possible violations of information causality by other sets of correlations, allowing us to certify when violations are not possible. We generalize the statement of information causality and reach a precise definition for the set of correlations satisfying this principle. We show that when searching for violations of information causality by physical theories, considering many copies is not necessary. Our aforementioned optimization framework approximates the information causality set from the outside. Conversely, we propose a different approach which allows us to approximate this set from the inside.
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.
Information causality states that the information obtainable by a receiver cannot be greater than the communication bits from a sender, even if they utilize no-signaling resources. This physical principle successfully explains some boundaries between quantum and postquantum nonlocal correlations, where the obtainable information reaches the maximum limit. We show that no-signaling resources of pure partially entangled states produce randomness (or noise) in the communication bits, and achievement of the maximum limit is impossible, i.e., the information causality principle is insufficient for the full identification of the quantum boundaries already for bipartite settings. The nonlocality inequalities such as so-called the Tsirelson inequality are extended to show how such randomness affects the strength of nonlocal correlations. As a result, a relation followed by most of quantum correlations in the simplest Bell scenario is revealed. The extended inequalities reflect the cryptographic principle such that a completely scrambled message cannot carry information.
Information causality (IC) was introduced as a physical principle that imposes constraints on the non-local correlations between two parties (Alice and Bob) in a Bell scenario. Specifically, it states that the information that Bob can gain about an n-bit database held by Alice is bounded by the information she communicates to him. To date, the question whether IC for any n∈N singles out the set of quantum correlations remains open, meaning that it is unknown whether for any number of inputs m and outputs d of the two parties the set of correlations that satisfy IC exactly coincides with the quantum correlations. In this work, we answer this question in the negative. Firstly, we show that for any finite database length n≥2, there is a bipartite set of correlations that satisfies IC for all compatible protocols and that exhibits post-quantum correlations in the Bell scenario with n+1 inputs and 2 outcomes per party. This result relies on constructing an entropic proof of IC for GPTs that may be of independent interest. We further show that in the Bell scenario with n+1 inputs and 2 outcomes per party, our constructed sets of correlations lead to neither a superset nor a subset of the quantum correlations. Secondly, we construct a set of correlations in the Bell scenario with 3 inputs and 2 outputs per party that satisfies IC (for all database sizes n∈N) and that includes post-quantum points. Consequently, all known formulations of information causality fail to fully characterize the bipartite set of quantum correlations, already in the 3-input, 2-outcome Bell scenario.
Recent developments in quantum information allow for a new understanding of quantum correlations. The aim of this paper is to physically explain why quantum mechanics obeys a stronger bond than the non-sig- naling requirement or alternatively why it obeys a principle of information causality. It is shown that a physical theory violating the quantum bond allows for correlations between settings while quantum mechanics only allows for correlations between possible outcomes. In fact, correlations between settings would violate the protocols used in quantum cryptography. The conclusion is that information codification is a local operation and quantum mechanics sets the general conditions for information exchanging in our universe since it satisfies and saturates the bond that is imposed by the principle of information causality, and in so doing it also sets specific constraints on both the possible interdependencies and the possible interactions (also causal interconnections) in our universe.