Information–theoretic implications of quantum causal structures

Chaves, Rafael; Majenz, Christian; Gross, David J.

doi:10.1038/ncomms6766

Cited by 160 publications

(246 citation statements)

References 51 publications

(104 reference statements)

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“…There, an algorithm is presented that, even though computationally demanding, computes all Shannon-type entropic inequalities for given marginal constraints. Furthermore, it has turned out that entropic inequalities are useful in quantum physics where they restrict possible theories of data generation in more general settings than the ones using Bell inequalities (see, e.g., [27][28][29][30]). Moreover, we would like to mention that meanwhile, information measures for causal inference among strings based on compression length have been proposed [31], thus extending the possible applications of inequalities like the ones presented in this article.…”

Section: Discussionmentioning

confidence: 99%

Information-Theoretic Inference of Common Ancestors

Steudel

2015

Entropy

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A directed acyclic graph (DAG) partially represents the conditional independence structure among observations of a system if the local Markov condition holds, that is if every variable is independent of its non-descendants given its parents. In general, there is a whole class of DAGs that represents a given set of conditional independence relations. We are interested in properties of this class that can be derived from observations of a subsystem only. To this end, we prove an information-theoretic inequality that allows for the inference of common ancestors of observed parts in any DAG representing some unknown larger system. More explicitly, we show that a large amount of dependence in terms of mutual information among the observations implies the existence of a common ancestor that distributes this information. Within the causal interpretation of DAGs, our result can be seen as a quantitative extension of Reichenbach's principle of common cause to more than two variables. Our conclusions are valid also for non-probabilistic observations, such as binary strings, since we state the proof for an axiomatized notion of "mutual information" that includes the stochastic as well as the algorithmic version.

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Section: Discussionmentioning

confidence: 99%

Information-Theoretic Inference of Common Ancestors

Steudel

2015

Entropy

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“…For instance, a complete description of the n-cycle is given by an exponential number of tight inequalities [20]. Entropic inequalities are able to describe extended Bell scenarios that define complicated non-convex sets in the probabilistic space of interest [27][28][29]. Entropic inequalities of the Bell type are attractive due to their capabilities in studies of setting with arbitrary number of outcomes and inefficiencies of measurement devices.…”

Section: Introductionmentioning

confidence: 99%

On generalized entropies and information-theoretic Bell inequalities under decoherence

Rastegin

2015

Annals of Physics

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We consider information-theoretic inequalities of the Bell type in the presence of decoherence. It is natural that too strong coupling with the environment can prevent an observation of quantum correlations. In this regard, the use of various entropic functions may give additional capabilities to reveal desired correlations. It was already shown that the Bell and Leggett-Garg inequalities in terms conditional Tsallis entropies are more sensitive in the cases of detection inefficiencies. In this paper, we study capabilities of generalized conditional entropies of the Tsallis type in analyzing the Bell theorem in decoherence scenarios. Two forms of the conditional Tsallis q-entropy are known in the literature. We show that each of them can be used for defining a metric in the probability space of interest. Such metrics can be used in realizing the so-called triangle principle. The triangle principle has recently been proposed as a unifying approach to questions of local realism and noncontextuality. Applying the triangle principle leads to the two families of q-metric inequalities of the Bell type. Information-theoretic formulations in terms of the q-entropic metrics are first discussed for the CHSH scenario in dephasing environment. Then we also revisit q-entropic inequalities of the Leggett-Garg type. An environmental influence is modeled by the phase damping channel and by the depolarizing channel.

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“…To investigate the origin of the right-hand side of Eq. (14), let us focus on the term H( m| xρ B ) omitted in the derivation of the IC principle (also in a generalization of the IC inequality [34]). …”

Section: ≤ H( M) − H( M| Xρ B ) ≤ H( M) (15)mentioning

confidence: 99%

Cryptographic quantum bound on nonlocality

Ishizaka

2017

Phys. Rev. A

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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.

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Information–theoretic implications of quantum causal structures

Cited by 160 publications

References 51 publications

Information-Theoretic Inference of Common Ancestors

Information-Theoretic Inference of Common Ancestors

On generalized entropies and information-theoretic Bell inequalities under decoherence

Cryptographic quantum bound on nonlocality

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