Information Causality Research Articles

Three-input majority function as the unique optimal function for the bias amplification using nonlocal boxes

Brassard et al. [Phys. Rev. Lett. 96, 250401 (2006)] showed that shared nonlocal boxes with the CHSH probability greater than $\frac{3+\sqrt{6}}6$ yields trivial communication complexity. There still exists the gap with the maximum CHSH probability $\frac{2+\sqrt{2}}4$ achievable by quantum mechanics. It is an interesting open question to determine the exact threshold for the trivial communication complexity. Brassard et al.'s idea is based on the recursive bias amplification by the 3-input majority function. It was not obvious if other choice of function exhibits stronger bias amplification. We show that the 3-input majority function is the unique optimal, so that one cannot improve the threshold $\frac{3+\sqrt{6}}6$ by Brassard et al.'s bias amplification. In this work, protocols for computing the function used for the bias amplification are restricted to be non-adaptive protocols or particular adaptive protocol inspired by Paw{\l}owski et al.'s protocol for information causality [Nature 461, 1101 (2009)]. We first show a new adaptive protocol inspired by Paw{\l}owski et al.'s protocol, and then show that the new adaptive protocol is better than any non-adaptive protocol. Finally, we show that the 3-input majority function is the unique optimal for the bias amplification if we apply the new adaptive protocol to each step of the bias amplification.

Information flow and causality as rigorous notions ab initio.

Information flow or information transfer the widely applicable general physics notion can be rigorously derived from first principles, rather than axiomatically proposed as an ansatz. Its logical association with causality is firmly rooted in the dynamical system that lies beneath. The principle of nil causality that reads, an event is not causal to another if the evolution of the latter is independent of the former, which transfer entropy analysis and Granger causality test fail to verify in many situations, turns out to be a proven theorem here. Established in this study are the information flows among the components of time-discrete mappings and time-continuous dynamical systems, both deterministic and stochastic. They have been obtained explicitly in closed form, and put to applications with the benchmark systems such as the Kaplan-Yorke map, Rössler system, baker transformation, Hénon map, and stochastic potential flow. Besides unraveling the causal relations as expected from the respective systems, some of the applications show that the information flow structure underlying a complex trajectory pattern could be tractable. For linear systems, the resulting remarkably concise formula asserts analytically that causation implies correlation, while correlation does not imply causation, providing a mathematical basis for the long-standing philosophical debate over causation versus correlation.

Exploring the joint measurability using an information-theoretic approach

We explore the legal purity parameters for the joint measurements. Instead of direct unsharpening the measurements, we perform the quantum cloning before the sharp measurements. The necessary fuzziness in the unsharp measurements is equivalently introduced in the imperfect cloning process. Based on the information causality and the consequent noisy nonlocal computation, one can derive the information-theoretic quadratic inequalities that must be satisfied by any physical theory. On the other hand, to guarantee the classicality, the linear Bell-type inequalities deduced by these quadratic ones must be obeyed. As for the joint measurability, the purity parameters must be chosen to obey both types of inequalities. Finally, the quadratic inequalities for purity parameters in the joint measurability region are derived.

Information Recovery and Causality: A Tribute to George Judge

In Professor George Judge's pursuit of information recovery and isolating causality in noisy effects observational data, there is a critical distinction between deductive and inductive empirical analysis. For the former, we bring together a synthesis of the literature that has emerged since Koopmans' measurement with theory philosophy. For the latter, we present a host of methodologies that attempt to isolate the causal mechanisms existing in patterns revealed in noisy measurement data. The deductive focus is limited by available theoretical constructs, whereas the inductive focus is fraught with data mining complications, ultimately finding its potential validation in forecasting.

Optical simulation of a Popescu-Rohrlich Box.

It is well known that the fair-sampling loophole in Bell test opened by the selection of the state to be measured can lead to post-quantum correlations. In this paper, we make the selection of the results after measurement, which opens the fair- sampling loophole too, and thus can lead to post-quantum correlations. This kind of result-selection loophole can be realized by pre- and post-selection processes within the “two-state vector formalism”, and a physical simulation of Popescu-Rohrlich (PR) box is designed in linear optical system. The probability distribution of the PR has a maximal CHSH value 4, i.e. it can maximally violate CHSH inequality. Because the “two-state vector formalism” violates the information causality, it opens the locality loophole too, which means that this kind of results selection within “two-state vector formalism” leads to both fair- sampling loophole and locality loophole, so we call it a comprehensive loophole in Bell test. The comprehensive loophole opened by the results selection within “two-state vector formalism” may be another possible explanation of why post-quantum correlations are incompatible with quantum mechanics and seem not to exist in nature.

Entropic Nonsignaling Correlations.

We introduce the concept of entropic nonsignaling correlations, i.e., entropies arising from probabilistic theories that are compatible with the fact that we cannot transmit information instantaneously. We characterize and show the relevance of these entropic correlations in a variety of different scenarios, ranging from typical Bell experiments to more refined descriptions such as bilocality and information causality. In particular, we apply the framework to derive the first entropic inequality testing genuine tripartite nonlocality in quantum systems of arbitrary dimension and also prove the first known monogamy relation for entropic Bell inequalities. Further, within the context of complex Bell networks, we show that entropic nonlocal correlations can be activated.

Dimensionality Reduction Method's Comparison Based on Statistical Dependencies

The field of machine learning deals with a huge amount of various algorithms, which are able to transform the observed data into many forms and dimensionality reduction (DR) is one of such transformations. There are many high quality papers which compares some of the DR's approaches and of course there other experiments which applies them with success. Not everyone is focused on information lost, increase of relevance or decrease of uncertainty during the transformation, which is hard to estimate and only few studies remark it briefly. This study aims to explain these inner features of four different DR's algorithms. These algorithms were not chosen randomly, but in purpose. It is chosen some representative from all of the major DR's groups. The comparison criteria are based on statistical dependencies, such as Correlation Coefficient, Euclidean Distance, Mutual Information and Granger causality. The winning algorithm should reasonably transform the input dataset with keeping the most of the inner dependencies.

Application of transfer entropy to causality detection and synchronization experiments in tokamaks

Determination of causal-effect relationships can be a difficult task even in the analysis of time series. This is particularly true in the case of complex, nonlinear systems affected by significant levels of noise. Causality can be modelled as a flow of information between systems, allowing to better predict the behaviour of a phenomenon on the basis of the knowledge of the one causing it. Therefore, information theoretic tools, such as the transfer entropy, have been used in various disciplines to quantify the causal relationship between events. In this paper, Transfer Entropy is applied to determining the information relationship between various phenomena in Tokamaks. The proposed approach provides unique insight about information causality in difficult situations, such as the link between sawteeth and ELMs and ELM pacing experiments. The application to the determination of disruption causes, and therefore to the classification of disruption types, looks also very promising. The obtained results indicate that the proposed method can provide a quantitative and statistically sound criterion to address the causal-effect relationships in various difficult and ambiguous situations if the data is of sufficient quality.

Local randomness in Cabello’s non-locality argument from the information causality principle

The principle of non-violation of "information causality", has been proposed as one of the foundational properties of nature\cite{nature}. The main goal of the paper is to explore the gap between quantum mechanical correlations and those allowed by "information causality" in the context of local randomness by using Cabello's nonlocality argument. This is interesting because the gap is slightly different than in the context of Hardy's similar nonlocality argument\cite{gazi}

Multi‐level Bell‐Type Inequality from Information Causality and Noisy Computations

In this paper, we show how information causality leads to Tsirelson bounds in a much easier way. Furthermore, a series of new Tsirelson bounds are then derived. We then define the communication protocols based on Random access code (RAC) and No-signaling box (NS-box) and then derive the objects for the communication complexity of symmetric quantum channels with i.i.d.(independent identically distribution) and uniform input marginal probabilities, consequently we obtain the multi-level Bell-type inequality. Deep ramifications concerning non-local quantum computation are also found and discussed.

Almost quantum correlations.

Quantum theory is not only successfully tested in laboratories every day but also constitutes a robust theoretical framework: small variations usually lead to implausible consequences, such as faster-than-light communication. It has even been argued that quantum theory may be special among possible theories. Here we report that, at the level of correlations among different systems, quantum theory is not so special. We define a set of correlations, dubbed 'almost quantum', and prove that it strictly contains the set of quantum correlations but satisfies all-but-one of the proposed principles to capture quantum correlations. We present numerical evidence that the remaining principle is satisfied too.

Information–theoretic implications of quantum causal structures

It is a relatively new insight of classical statistics that empirical data can contain information about causation rather than mere correlation. First algorithms have been proposed that are capable of testing whether a presumed causal relationship is compatible with an observed distribution. However, no systematic method is known for treating such problems in a way that generalizes to quantum systems. Here, we describe a general algorithm for computing information-theoretic constraints on the correlations that can arise from a given causal structure, where we allow for quantum systems as well as classical random variables. The general technique is applied to two relevant cases: first, we show that the principle of information causality appears naturally in our framework and go on to generalize and strengthen it. Second, we derive bounds on the correlations that can occur in a networked architecture, where a set of few-body quantum systems is distributed among some parties.

Dimension of physical systems, information processing, and thermodynamics

We ask how quantum theory compares to more general physical theories from the point of view of dimension. To do so, we first give two model-independent definitions of the dimension of physical systems, based on measurements and the capacity of storing information. While both definitions are equivalent in classical and quantum mechanics, they are different in generalized probabilistic theories. We discuss in detail the case of a theory known as ‘boxworld’, and show that such a theory features systems with dimension mismatch. This dimension mismatch can be made arbitrarily large using an amplification procedure. Furthermore, we show that the dimension mismatch of boxworld has strong consequences on its power for performing information-theoretic tasks, leading to the collapse of communication complexity and to the violation of information causality. Finally, we discuss the consequences of a dimension mismatch from the perspective of thermodynamics, and ask whether this effect could break Landauerʼs erasure principle and thus the second law.

Information causality in the quantum and post-quantum regime.

Quantum correlations can be stronger than anything achieved by classical systems, yet they are not reaching the limit imposed by relativity. The principle of information causality offers a possible explanation for why the world is quantum and why there appear to be no even stronger correlations. Generalizing the no-signaling condition it suggests that the amount of accessible information must not be larger than the amount of transmitted information. Here we study this principle experimentally in the classical, quantum and post-quantum regimes. We simulate correlations that are stronger than allowed by quantum mechanics by exploiting the effect of polarization-dependent loss in a photonic Bell-test experiment. Our method also applies to other fundamental principles and our results highlight the special importance of anisotropic regions of the no-signalling polytope in the study of fundamental principles.

Editorial Comment on the Special Issue of “Information in Dynamical Systems and Complex Systems”

This special issue collects contributions from the participants of the “Information in Dynamical Systems and Complex Systems” workshop, which cover a wide range of important problems and new approaches that lie in the intersection of information theory and dynamical systems. The contributions include theoretical characterization and understanding of the different types of information flow and causality in general stochastic processes, inference and identification of coupling structure and parameters of system dynamics, rigorous coarse-grain modeling of network dynamical systems, and exact statistical testing of fundamental information-theoretic quantities such as the mutual information. The collective efforts reported here in reflect a modern perspective of the intimate connection between dynamical systems and information flow, leading to the promise of better understanding and modeling of natural complex systems and better/optimal design of engineering systems.

Information and communication in polygon theories

Generalized probabilistic theories (GPT) provide a framework in which one can formulate physical theories that includes classical and quantum theories, but also many other alternative theories. In order to compare different GPTs, we advocate an approach in which one views a state in a GPT as a resource, and quantifies the cost of interconverting between different such resources. We illustrate this approach on polygon theories (Janotta et al. New J. Phys 13, 063024, 2011) that interpolate (as the number n of edges of the polygon increases) between a classical trit (when n=3) and a real quantum bit (when n=infinity). Our main results are that simulating the transmission of a single n-gon state requires more than one qubit, or more than log(log(n)) bits, and that n-gon states with n odd cannot be simulated by n'-gon states with n' even (for all n,n'). These results are obtained by showing that the classical capacity of a single n-gon state with n even is 1 bit, whereas it is larger than 1 bit when n is odd; by showing that transmitting a single n-gon state with n even violates information causality; and by showing studying the communication complexity cost of the nondeterministic not equal function using n-gon states.

Entanglement, Information, Causality

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.

Local orthogonality provides a tight upper bound for Hardy's nonlocality

The amount of nonlocality in quantum theory is limited compared to that allowed in generalized no-signaling theory [S. Popescu and D. Rohrlich, Found. Phys. 24, 379 (1994)]. This feature, for example, gets manifested in the amount of Bell inequality violation as well as in the degree of success probability of Hardy's (Cabello's) nonlocality argument. Physical principles like information causality and macroscopic locality have been proposed for analyzing restricted nonlocality in quantum mechanics, viz. explaining the Cirel'son bound. However, these principles are not very successful in explaining the maximum success probability of Hardy's as well as Cabello's argument in quantum theory. Here we show that a recently proposed physical principle, namely local orthogonality, does better by providing a tighter upper bound on the success probability for Hardy's nonlocality. This bound is relatively closer to the corresponding quantum value compared to the bounds achieved from other principles.

Macroscopic locality with equal bias reproduces with high fidelity a quantum distribution achieving the Tsirelson's bound

Two physical principles, Macroscopic Locality (ML) and Information Causality (IC), so far, have been most successful in distinguishing quantum correlations from post-quantum correlations. However, there are also some post-quantum probability distributions which cannot be distinguished with the help of these principles. Thus, it is interesting to see whether consideration of these two principles, separately, along with some additional physically plausible constraints, can explain some interesting quantum features which are otherwise hard to reproduce. In this paper we show that, in a Bell-CHSH scenario, ML along with constraint of equal-biasness for the concerned observables, almost reproduces the quantum joint probability distribution corresponding to maximal quantum Bell violation, which is unique up to relabeling. From this example and earlier work of Cavalcanti, Salles and Scarani, we conclude that IC and ML are in-equivalent physical principles; satisfying one does not imply that the other is satisfied.

Multivariate Conditional Granger Causality Analysis for Lagged Response of Soil Respiration in a Temperate Forest

Ecological multivariate systems offer a suitable data set on which to apply recent advances in information theory and causality detection. These systems are driven by the interplay of various environmental factors: meteorological and hydrological forcing, which are often correlated with each other at different time lags; and biological factors, primary producers and decomposers with both autonomous and coupled dynamics. Here, using conditional spectral Granger causality, we quantify directional causalities in a complex atmosphere-plant-soil system involving the carbon cycle. Granger causality is a statistical approach, originating in econometrics, used to identify the presence of linear causal interactions between time series of data, based on prediction theory. We first test to see if there was a significant difference in the causal structure among two treatments where carbon allocation to roots was interrupted by girdling. We then expanded the analysis, introducing radiation and soil moisture. The results showed a complex pattern of multilevel interactions, with some of these interactions depending upon the number of variables in the system. However, no significant differences emerged in the causal structure of above and below ground carbon cycle among the two treatments.