Hannover 2016 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 37: Quantum Information: Concepts and Methods VI
Q 37.2: Vortrag
Mittwoch, 2. März 2016, 14:45–15:00, e214
Information Inequalities for Classical and Quantum Networks — •Nikolai Miklin1, Rafael Chaves2, and Costantino Budroni1 — 1Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Str. 3, 57068 Siegen, Germany — 2Institute for Theoretical Physics, University of Cologne, 50937 Cologne, Germany
Causal dependencies among random variables can be investigated via information-theoretic quantities (e.g. Shannon entropy, mutual information, etc.): for unconstrained variables, their entropies form a convex cone and causal dependencies can be added as linear constraints [1]. However, such a method is computationally demanding in the case of restrictions on the observable variables (e.g., latent variables, marginal scenarios), since it involves the projection of the entropy cone via the Fourier-Motzkin method, which has a double exponential complexity [2]. Actual computation has been performed in case of few variables.
To overcome such problems, we develop alternative techniques (e.g. based on adhesivity of entropies [3]) able to completely characterize scenarios with higher number of variables. Finally, we apply these techniques to investigated several new causal structures associated both with classical and quantum scenarios such as Bell scenarios, classical and quantum networks.
[1] R. Chaves, et al. Proc UAI 2014, pp. 112 - 121, AUAI Press, 2014
[2] A. Schrijver, Theory of Linear and Integer Programming, John Wiley & sons, 1998
[3] F. Matúš, Discrete Mathematics 307.21, 2007