Information Causality Research Articles

Bound on Hardy’s nonlocality 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.

Entropy and information causality in general probabilistic theories

We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality (IC) recently proposed by Pawlowski et al (2009 arXiv:0905.2292). We consider two entropic quantities, which we term measurement and mixing entropy. In the context of classical and quantum theory, these coincide, being given by the Shannon and von Neumann entropies, respectively; in general, however, they are very different. In particular, while measurement entropy is easily seen to be concave, mixing entropy need not be. In fact, as we show, mixing entropy is not concave whenever the state space is a non-simplicial polytope. Thus, the condition that measurement and mixing entropies coincide is a strong constraint on possible theories. We call theories with this property monoentropic.Measurement entropy is subadditive, but not in general strongly subadditive. Equivalently, if we define the mutual information between two systems A and B by the usual formula I(A: B)=H(A)+H(B)-H(AB), where H denotes the measurement entropy and AB is a non-signaling composite of A and B, then it can happen that I(A:BC)<I(A:B). This is relevant to IC in the sense of Pawlowski et al: we show that any monoentropic non-signaling theory in which measurement entropy is strongly subadditive, and also satisfies a version of the Holevo bound, is informationally causal, and on the other hand we observe that Popescu–Rohrlich boxes, which violate IC, also violate strong subadditivity. We also explore the interplay between measurement and mixing entropy and various natural conditions on theories that arise in quantum axiomatics.

Entropy in general physical theories

Information plays an important role in our understanding of the physical world. Hence we propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical worlds, our measure reduces to the von Neumann and Shannon entropies, respectively. It can even be used in a quantum or classical setting where we are only allowed to perform a limited set of operations. In a world that admits superstrong correlations in the form of non-local boxes, our measure can be used to analyze protocols such as superstrong random access encodings and the violation of ‘information causality’. However, we also show that in such a world no entropic measure can exhibit all the properties we commonly accept in a quantum setting. For example, there exists no ‘reasonable’ measure of conditional entropy that is subadditive. Finally, we prove a coding theorem for some theories that is analogous to the quantum and classical settings, providing us with an appealing operational interpretation.

Differentiating information transfer and causal effect

The concepts of information transfer and causal effect have received much recent attention, yet often the two are not appropriately distinguished and certain measures have been suggested to be suitable for both. We discuss two existing measures, transfer entropy and information flow, which can be used separately to quantify information transfer and causal information flow respectively. We apply these measures to cellular automata on a local scale in space and time, in order to explicitly contrast them and emphasize the differences between information transfer and causality. We also describe the manner in which the measures are complementary, including the conditions under which they in fact converge. We show that causal information flow is a primary tool to describe the causal structure of a system, while information transfer can then be used to describe the emergent computation on that causal structure.

Recovering part of the boundary between quantum and nonquantum correlations from information causality

Recently, the principle of information causality has appeared as a good candidate for an information-theoretic principle that would single out quantum correlations among more general nonsignaling models. Here, we present results going in this direction, namely, we show that part of the boundary of quantum correlations actually emerges from information causality.

Information causality as a physical principle

Quantum physics has remarkable distinguishing characteristics. For example, it gives only probabilistic predictions (non-determinism) and does not allow copying of unknown states (no-cloning). Quantum correlations may be stronger than any classical ones, but information cannot be transmitted faster than light (no-signalling). However, these features do not uniquely define quantum physics. A broad class of theories exist that share such traits and allow even stronger (than quantum) correlations. Here we introduce the principle of 'information causality' and show that it is respected by classical and quantum physics but violated by all no-signalling theories with stronger than (the strongest) quantum correlations. The principle relates to the amount of information that an observer (Bob) can gain about a data set belonging to another observer (Alice), the contents of which are completely unknown to him. Using all his local resources (which may be correlated with her resources) and allowing classical communication from her, the amount of information that Bob can recover is bounded by the information volume (m) of the communication. Namely, if Alice communicates m bits to Bob, the total information obtainable by Bob cannot be greater than m. For m = 0, information causality reduces to the standard no-signalling principle. However, no-signalling theories with maximally strong correlations would allow Bob access to all the data in any m-bit subset of the whole data set held by Alice. If only one bit is sent by Alice (m = 1), this is tantamount to Bob's being able to access the value of any single bit of Alice's data (but not all of them). Information causality may therefore help to distinguish physical theories from non-physical ones. We suggest that information causality-a generalization of the no-signalling condition-might be one of the foundational properties of nature.

Information transmission and causality in the Italian Treasury bond market

We examine causality and efficiency in the Italian T-bond market, where cash trades take place on the domestic Mercato Telematico dei Titoli di Stato, while futures trading is based on the London International Financial Futures Exchange. We find evidence that causality in prices runs in both directions, and that the cash lead is almost comparable in size and extension to the futures lead. We then try to assess whether the cash market is weak-form efficient with respect to LIFFE prices. Using a simple trading rule with a variety of time and price filters, we conclude that the observed lead cannot be exploited to make a profit after transaction costs.

Information Transmission and Causality in the Italian Treasury Bond Market

I examine causality and efficiency in the Italian Treasury bond market, where cash trades take place on the domestic Mercato dei Titoli di Stato, while futures trading is based on the London International Financial Futures Exchange. I find evidence that causality in prices runs in both directions, and that the cash lead is almost comparable in size and extension to the futures lead. I then try to assess whether the cash market is weak-form efficient with respect to LIFFE prices. Using a simple trading rule with a variety of time and price filters, I conclude that the observed lead cannot be exploited to make a profit after accounting for transaction costs.

Medical Knowledge: The Essential of Causality Assessment

As drug-induced disorders now occupy an increasing place in the activities of the pharmaceutical industry and the regulators, as well as in the diagnostic process of prescribers, every practitioner should ask himself whether the occurrence of an abnormality is the consequence of the treated disease or of its treatment. This is particularly true in the domains which are the main targets of drug toxicity, such as skin, blood, and liver, but it applies to all other clinical or laboratory abnormalities as well. Therefore, a physician must be aware of the most frequent causes of abnormalities and the simplest tests to detect them. Three examples of the advantages of the medical approach for diagnosis of adverse drug reactions demonstrate that quality of information and drug causality assessment are inseparable.

Information Structures, Causality, and Nonsequential Stochastic Control I: Design-Independent Properties

In control theory, the usual notion of causality---that, at all times, a system's output (action) only depends on its past and present inputs (observations)---presupposes that all inputs and outputs can be ordered, a priori, in time. In reality, many distributed systems (those subject to deadlock, for instance), are not sequential in this sense. In a previous paper (part I) [SIAM J. Control Optim., 30 (1992), pp. 1447--1475], the relationship between a less restrictive notion of causality, deadlock-freeness, and the design-independent properties of a potentially nonsequential generic stochastic control problem formulated within the framework of Witsenhausen's intrinsic model was explored. In the present paper (part II) the properties of individual designs are examined. In particular, a property of a design's information partition that is necessary and sufficient to ensure its deadlock-freeness is identified and shown to be sufficient to ensure its possession of an expected reward. It is also shown, by example, that there exist nontrivial deadlock-free designs that cannot be associated with any deadlock-free information structure. The first result provides an intuitive design-dependent characterization of the cause/effect notion of causality and suggests a framework for the optimization of constrained nonsequential stochastic control problems. The second implies that this characterization is finer than existing design-independent characterizations, including properties C (Witsenhausen) and CI (part I).