The paper is divided in two parts. In the first one a summary of the main issues about quantum non–locality is provided. In the second part, the connections with information and causality are considered. In particular, it is shown that a principle of information causality implies that hyper–correlations among experimental settings are not possible but only correlations among possible outcomes. Since a setting is for measuring a particular observable and the eigenbasis of this observable can be considered a code, this means that information codification is a local procedure.
The paper is divided in two parts. In the first one a summary of the main issues about quantum non–locality is provided. In the second part, the connections with information and causality are considered. In particular, it is shown that a principle of information causality implies that hyper–correlations among experimental settings are not possible but only correlations among possible outcomes. Since a setting is for measuring a particular observable and the eigenbasis of this observable can be considered a code, this means that information codification is a local procedure.
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.
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.
Recent works in foundations of quantum (field) theory and relativistic quantum information try to better grasp the interplay between the structure of quantum correlations and the constraints imposed by causality on physical operations. Chapter 1 is dedicated to the study of the conceptual implications of quantum nonlocality, a concept that subsumes that of entanglement in a certain way. We detail the recent information-theoretic approaches to understanding the structure of nonlocal correlations, and the issues the latter raise concerning the ability of local observers to isolate a system from its environment. Chapter 2 reviews in what sense imposing Poincare invariance affects entanglement detection and quantification procedures. This invariance ultimately forces a description of all quantum systems within the framework of quantum field theory, which leads to the impossibility of localized finite-energy states and to the divergence of all entanglement measures for local observers. We provide a solution to these two problems by showing that there exists a generic equivalence between a finite spatial resolution of the measurement apparatus and the exclusion of high-energy degrees of freedom from the definition of the observed system. This equivalence allows for an epistemic interpretation of the standard quantum formalism describing nonrelativistic localized systems and their correlations, hence a clarification of the origin of the finite measures of entanglement between such systems. Chapter 3 presents a recent theoretical framework that predicts the existence of correlations with indefinite causal order. In analogy to the information-theoretic approaches to nonlocal correlations, we introduce some principles that constrain the structure of such correlations, which is a first step toward a clear understanding of their physical origin.
At the basis of the problem of explaining non-local quantum correlations lies the tension between two factors: on the one hand, the natural interpretation of correlations as the manifestation of a causal relation; on the other, the resistance on the part of the physics underlying said correlations to adjust to the most essential features of a pre-theoretic notion of causation. In this paper, I argue for the rejection of the first horn of the dilemma, i.e., the assumption that quantum correlations call for a causal explanation. The paper is divided into two parts. The first, destructive, part provides a critical overview of the enterprise of causally interpreting non-local quantum correlations, with the aim of warning against the temptation of an account of causation claiming to cover such correlations 'for free'. The second, constructive, part introduces the so-called structural explanation (a variety of non-causal explanation that shows how the explanandum is the manifestation of a fundamental structure of the world) and argues that quantum correlations might be explained structurally in the context of an information-theoretic approach to QT.
Understanding the concept of causality is fundamental in physics, as it conditions the very possibility of any exchange of information between physical systems. This article examines and compares three main interpretations of the correlative operational concept of "causal separation" that have been respectively proposed in special relativity, quantum theory, and according to the statistical "non-signalling" condition. These interpretations, which can be classified regarding the range of CHSH correlation degrees they allow, lead to radically different results regarding the exchange of information between physical systems. Namely, it can be shown that, in opposition with the non-communication theorem of quantum theory, non-local communication can be established between the two entangled parts of a physical system when the relativistic criterium of causal separation is satisfied but not the quantum one.
This paper shows the possibility of non-local communication between two entangled, spacelike separated sub-systems. More specifically, it is shown that if there exist (at least) two non-commuting observables respectively defined on these two sub-systems then, for some entangled state of the global system, the probability distribution of the outcomes of measurements performed in one of its parts is changed by the actions that have been performed in the other one. This causal dependency, which includes that of the settings, makes possible a nonlocal exchange of information between the parties.