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.
Steady technological advances are paving the way for the implementation of the quantum internet, a network of locations interconnected by quantum channels. Here we propose a model to simulate a ...quantum internet based on optical fibers and employ network-theory techniques to characterize the statistical properties of the photonic networks it generates. Our model predicts a continuous phase transition between a disconnected and a highly connected phase and that the typical photonic networks do not present the small world property. We compute the critical exponents characterizing the phase transition, provide quantitative estimates for the minimum density of nodes needed to have a fully connected network and for the average distance between nodes. Our results thus provide quantitative benchmarks for the development of a quantum internet.
Bell's theorem was a cornerstone for our understanding of quantum theory and the establishment of Bell non-locality played a crucial role in the development of quantum information. Recently, its ...extension to complex networks has been attracting growing attention, but a deep characterization of quantum behavior is still missing for this novel context. In this work we analyze quantum correlations arising in the bilocality scenario, that is a tripartite quantum network where the correlations between the parties are mediated by two independent sources of states. First, we prove that non-bilocal correlations witnessed through a Bell-state measurement in the central node of the network form a subset of those obtainable by means of a local projective measurement. This leads us to derive the maximal violation of the bilocality inequality that can be achieved by arbitrary two-qubit quantum states and arbitrary local projective measurements. We then analyze in details the relation between the violation of the bilocality inequality and the CHSH inequality. Finally, we show how our method can be extended to the n-locality scenario consisting of n two-qubit quantum states distributed among n + 1 nodes of a star-shaped network.
Bell's theorem plays a crucial role in quantum information processing and thus several experimental investigations of Bell inequalities violations have been carried out over the years. Despite their ...fundamental relevance, however, previous experiments did not consider an ingredient of relevance for quantum networks: the fact that correlations between distant parties are mediated by several, typically independent sources. Here, using a photonic setup, we investigate a quantum network consisting of three spatially separated nodes whose correlations are mediated by two distinct sources. This scenario allows for the emergence of the so-called non-bilocal correlations, incompatible with any local model involving two independent hidden variables. We experimentally witness the emergence of this kind of quantum correlations by violating a Bell-like inequality under the fair-sampling assumption. Our results provide a proof-of-principle experiment of generalizations of Bell's theorem for networks, which could represent a potential resource for quantum communication protocols.
Bell's theorem in physics, as well as causal discovery in machine learning, both face the problem of deciding whether observed data is compatible with a presumed causal relationship between the ...variables (for example, a local hidden variable model). Traditionally, Bell inequalities have been used to describe the restrictions imposed by causal structures on marginal distributions. However, some structures give rise to non-convex constraints on the accessible data, and it has recently been noted that linear inequalities on the observable entropies capture these situations more naturally. In this paper, we show the versatility of the entropic approach by greatly expanding the set of scenarios for which entropic constraints are known. For the first time, we treat Bell scenarios involving multiple parties and multiple observables per party. Going beyond the usual Bell setup, we exhibit inequalities for scenarios with extra conditional independence assumptions, as well as a limited amount of shared randomness between the parties. Many of our results are based on a geometric observation: Bell polytopes for two-outcome measurements can be naturally imbedded into the convex cone of attainable marginal entropies. Thus, any entropic inequality can be translated into one valid for probabilities. In some situations the converse also holds, which provides us with a rich source of candidate entropic inequalities.
Moringa oleifera
seeds contain a water-soluble lectin water-soluble
M. oleifera
lectin (WSMoL) that has shown coagulant activity. Magnesium ions are able to interfere with the ability of this lectin ...to bind carbohydrates. In this study, we performed structural characterization of WSMoL and analyzed its effect on the electrical resistance of a kaolin clay suspension in both presence and absence of monosaccharides (
N
-acetylglucosamine, glucose, or fructose) and magnesium ions. The coagulant activity of WSMoL was monitored by measuring optical density and electrical resistance over a period of 60 min. Native WSMoL had a molecular mass of 60 kDa and exhibited anionic nature (pI 5.5). In sodium dodecyl sulfate–polyacrylamide gel electrophoresis (SDS-PAGE), it appeared as three polypeptide bands of 30, 20, and 10 kDa. WSMoL reduced the optical density and electrical resistance of the kaolin suspension, which suggests that suspended particles are destabilized and that this is followed by formation of complexes. The coagulant activity of lectin decreased in the presence of Mg
2+
ions and carbohydrates at concentrations that also inhibited hemagglutinating activity. This was most likely due to conformational changes in lectin structure. Our findings suggest that the coagulant activity of WSMoL is enhanced by lowering of electrical resistance of the medium and is impaired by lectin–carbohydrate and lectin–Mg
2+
interactions.
We postulate a principle stating that the initial condition of a physical system is typically algorithmically independent of the dynamical law. We discuss the implications of this principle and argue ...that they link thermodynamics and causal inference. On the one hand, they entail behavior that is similar to the usual arrow of time. On the other hand, they motivate a statistical asymmetry between cause and effect that has recently been postulated in the field of causal inference, namely, that the probability distribution P cause contains no information about the conditional distribution P effect cause and vice versa, while P effect may contain information about P cause effect .
The launch of a satellite capable of distributing entanglement through long distances and the first loophole-free violation of Bell inequalities are milestones indicating a clear path for the ...establishment of quantum networks. However, nonlocality in networks with independent entanglement sources has only been experimentally verified in simple tripartite networks, via the violation of bilocality inequalities. Here, by using a scalable photonic platform, we implement star-shaped quantum networks consisting of up to five distant nodes and four independent entanglement sources. We exploit this platform to violate the chained n-locality inequality and thus witness, in a device-independent way, the emergence of nonlocal correlations among the nodes of the implemented networks. These results open new perspectives for quantum information processing applications in the relevant regime where the observed correlations are compatible with standard local hidden variable models but are non-classical if the independence of the sources is taken into account.
In a Bell experiment, it is natural to seek a causal account of correlations wherein only a common cause acts on the outcomes. For this causal structure, Bell inequality violations can be explained ...only if causal dependencies are modeled as intrinsically quantum. There also exists a vast landscape of causal structures beyond Bell that can witness nonclassicality, in some cases without even requiring free external inputs. Here, we undertake a photonic experiment realizing one such example: the triangle causal network, consisting of three measurement stations pairwise connected by common causes and no external inputs. To demonstrate the nonclassicality of the data, we adapt and improve three known techniques: (i) a machine-learning-based heuristic test, (ii) a data-seeded inflation technique generating polynomial Bell-type inequalities and (iii) entropic inequalities. The demonstrated experimental and data analysis tools are broadly applicable paving the way for future networks of growing complexity.
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