Macroscopically local correlations can violate information causality

Although quantum mechanics is a very successful theory, its foundations are still a subject of intense debate. One of the main problems is the fact that quantum mechanics is based on abstract mathematical axioms, rather than on physical principles. Quantum information theory has recently provided new ideas from which one could obtain physical axioms constraining the resulting statistics one can obtain in experiments. Information causality and macroscopic locality are two principles recently proposed to solve this problem. However none of them were proven to define the set of correlations one can observe. In this paper, we present an extension of information causality and study its consequences. It is shown that the two above-mentioned principles are inequivalent: if the correlations allowed by nature were the ones satisfying macroscopic locality, information causality would be violated. This gives more confidence in information causality as a physical principle defining the possible correlation allowed by nature.Comment: are welcome. 6 pages, 4 figs. This is the originally submitted version. The published version contains some bounds on quantum realizations of d2dd isotropic boxes (table 1), found by T. Vertesi, who kindly shared them with u

Causality and Intrinsic Information

This text will discuss the concept of information and its relevance in the study of the nature of the mind. It will analyze a hypothesis that deals with the equivalence between information and causality, which results in information having a double ontological character: “intrinsic” and “extrinsic.” A discussion will follow on Integrated Information Theory, which is developed from a variation of this thesis. It will be proposed that this theory does not reach the objective of being an “intrinsic” information theory, precisely because it is an adaptation of classical information theory. For this reason, it neither allows nor avoids the paradoxes of the subject–object distinction, nor shows how the causal evolution of an integrated system can be treated in informational terms; that is, it cannot unite causality and information

Causal conditioning and instantaneous coupling in causality graphs

The paper investigates the link between Granger causality graphs recently formalized by Eichler and directed information theory developed by Massey and Kramer. We particularly insist on the implication of two notions of causality that may occur in physical systems. It is well accepted that dynamical causality is assessed by the conditional transfer entropy, a measure appearing naturally as a part of directed information. Surprisingly the notion of instantaneous causality is often overlooked, even if it was clearly understood in early works. In the bivariate case, instantaneous coupling is measured adequately by the instantaneous information exchange, a measure that supplements the transfer entropy in the decomposition of directed information. In this paper, the focus is put on the multivariate case and conditional graph modeling issues. In this framework, we show that the decomposition of directed information into the sum of transfer entropy and information exchange does not hold anymore. Nevertheless, the discussion allows to put forward the two measures as pillars for the inference of causality graphs. We illustrate this on two synthetic examples which allow us to discuss not only the theoretical concepts, but also the practical estimation issues.Comment: submitte

ELG hypothesis is valid for India: An Evidence from Structural Causality

Causality is important for empirical analysis in economics but not easily detected. Therefore, it is always important that one should investigate the problem not only on statistical grounds but also add extra statistical information which may come from economic events happening over a time about the problem under study. This extra statistical information helps in introducing asymmetry in the relationship. Most of the studies are based on Granger Causality for determining causal direction between export and economic growth for individual countries. In this paper we use a method suggested by Hoover (2001) for detecting causality which incorporates extra statistical information, economic theory and statistical analysis. We apply this technique to a simulated data and also apply it to the export-led growth hypothesis for India. Our results indicate that there is unidirectional causality from export to economic growth.Structural Causality, Conditional and Marginal probability distributions, Granger Causality, Export Led Economic Growth

Space Time relaying versus Information Causality

We investigate the connection between causality and Information Theory. We show that a simple reading of Information Theory makes that quantum entanglement allows super-luminal information transfer. We show that introducing the concept of space-time information relaying partially solves the paradox of non causal information transfer. Surprisingly information causality is only dependent on the quantum unitarity which is a weaker principle than physical causality

On directed information theory and Granger causality graphs

Directed information theory deals with communication channels with feedback. When applied to networks, a natural extension based on causal conditioning is needed. We show here that measures built from directed information theory in networks can be used to assess Granger causality graphs of stochastic processes. We show that directed information theory includes measures such as the transfer entropy, and that it is the adequate information theoretic framework needed for neuroscience applications, such as connectivity inference problems.Comment: accepted for publications, Journal of Computational Neuroscienc

Bound on Hardy's non-locality from the principle of Information Causality

Recently,the principle of nonviolation of information causality [Nature 461,1101 (2009)], has been proposed as one of the foundational properties of nature. We explore the Hardy's nonlocality theorem for two qubit systems, in the context of generalised probability theory, restricted by the principle of nonviolation of information causality. Applying, a sufficient condition for information causality violation, we derive an upper bound on the maximum success probability of Hardy's nonlocality argument. We find that the bound achieved here is higher than that allowed by quantum mechanics,but still much less than what the nosignaling condition permits. We also study the Cabello type nonlocality argument (a generalization of Hardy's argument) in this context.Comment: Abstract modified, changes made in the conclusion, throughout the paper we clarified that the condition used by us is protocal based and is only a sufficient condition for the violation of information causalit

Identifying interactions in the time and frequency domains in local and global networks : a Granger causality approach

Background Reverse-engineering approaches such as Bayesian network inference, ordinary differential equations (ODEs) and information theory are widely applied to deriving causal relationships among different elements such as genes, proteins, metabolites, neurons, brain areas and so on, based upon multi-dimensional spatial and temporal data. There are several well-established reverse-engineering approaches to explore causal relationships in a dynamic network, such as ordinary differential equations (ODE), Bayesian networks, information theory and Granger Causality. Results Here we focused on Granger causality both in the time and frequency domain and in local and global networks, and applied our approach to experimental data (genes and proteins). For a small gene network, Granger causality outperformed all the other three approaches mentioned above. A global protein network of 812 proteins was reconstructed, using a novel approach. The obtained results fitted well with known experimental findings and predicted many experimentally testable results. In addition to interactions in the time domain, interactions in the frequency domain were also recovered. Conclusions The results on the proteomic data and gene data confirm that Granger causality is a simple and accurate approach to recover the network structure. Our approach is general and can be easily applied to other types of temporal data