I present our work on inferring causality in the classical world and encourage the audience to think about possible generalizations to the quantum world. Statistical dependences between observed quantities X and Y indicate a causal relation, but it is a priori not clear whether X caused Y or Y caused X or there is a common cause of both. It is widely believed that this can only be decided if either one is able to do interventions on the system, or if X and Y are part of a larger set of variables. In the latter case, conditional statistical independences contain some information on causal directions, formalized by the Causal Markov Condition on directed acyclic graphs. Contrary to this belief, we have shown that empirical joint distributions of just two variables often indicate the causal direction. The observed asymmetry between cause and effect is, on the one hand, related to the thermodynamic arrow of time. On the other hand, it can be derived from a new principle that we have postulated: the Algorithmic Causal Markov Condition, which relates Kolmogorov complexity to causality.
Literature:  Janzing, Schoelkopf: Causal inference using the algorithmic Markov condition, IEEE TIT 2010.
 Daniusis, Janzing,...: Inferring deterministic causal relations, UAI 2010.
 Janzing: On the entropy production of time-series with uni-directional linearity.Journ. Stat. Phys. 2010.