Mainz 2017 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 8: Quantum Information: Concepts and Methods II
Q 8.2: Vortrag
Montag, 6. März 2017, 17:15–17:30, P 2
Indistinguishability of causal relations from limited marginals — Costantino Budroni1, •Nikolai Miklin1, and Rafael Chaves2 — 1Universität Siegen, Walter-Flex-Str. 3 , 57068 Siegen, Germany — 2International Institute of Physics, 59070 - 405 Natal, Brazil
Deciding global properties of a given object from partial information is a problem often encountered in the most diverse fields. In probability theory this problem is known as the marginal problem: deciding whether a given set of marginal probability distributions for some random variables arises from a joint distribution of all these variables. Another important problem is of a causal inference which arises in many cases together with the marginal problem. This problem questions whether observed correlations are compatible with some underlined causal structure.
We investigate the possibility of distinguishing among different causal relations starting from a limited set of marginals. Our main tool is the notion of adhesivity, that is, the extension of probability or entropies defined only on subsets of variables, which provides additional independence constraints among them. Our results provide a criterion for recognizing which causal structures are indistinguishable when only limited marginal information is accessible. Furthermore, the existence of such extensions greatly simplifies the characterization of a marginal scenario, a result that facilitates the derivation of Bell inequalities both in the probabilistic and entropic frameworks, and the identification of marginal scenarios where classical, quantum, and postquantum probabilities coincide.