**November 19, 2014**

Today we have a new paper out on the arXiv, linking the curious phenomenon of nonlocality in quantum physics to techniques from causal inference: https://arxiv.org/abs/1411.4648 .

In medicine, one would often like to know whether something is the cause of something else. For example, whether a drug remedies a given symptom or whether a given food leads to a certain illness. When possible, one would like to distinguish between causation and mere correlation. For example, diabetes is associated with high blood pressure. But is high blood pressure causing diabetes? Or does diabetes cause high blood pressure? Or is there perhaps some common factor which causes both of them? The field of causality, which is a relatively young subfield of probability theory and statistics, deals with this kind of questions in rigorous mathematical terms. In particular, there is an elegant graphical approach, which makes such questions clear by expressing them in terms of, well… graphs! In our paper, we borrow the machinery from causality and apply it in a very different setting – quantum physics.

In quantum physics, observations can be at odds with our everyday understanding of the world. By measuring on particles in so-called entangled states, two separate experimenters can obtain correlated data which is not compatible with any classical explanation that obeys a few, very natural assumptions. In particular, (i) that each experimenter can choose freely what measurement to make, independent of the other experimenter and of how the particles were prepared, and (ii) that the results obtained by one experimenter cannot be influenced by any action of the other. These can be understood as assumptions about the causal structure of the experiment: (i) says that the other experimenter, or the source of particles, cannot be causes of first experimenter’s choice of measurement. (ii) says e.g. that the first experimenter’s measurement choice cannot be a cause of the other experimenter’s outcome. Any classical model which attempts to explain the observations in terms of underlying variables and which obeys (i) and (ii) is bound to fail. This was first pointed out by John Bell in the 60s, and has by now been confirmed in lots of experiments. The fact that such classical models can be ruled out by experimental observation is both a marvel of nature, and also the basis for quantum cryptography and random number generation, which I have recently written about.

In this paper, we develop a framework for dealing with the ways that different causal models restrict possible observations in a systematic and quantifiable way. Causal models can be represented systematically using graphs, which represent Bayesian networks. Essentially, one draws a picture with a symbol for each of the relevant parameters, such as the experimenter’s measurement choices and outcomes, and the underlying classical variables, and then draws arrows between them representing possible cause and effect. Based on such pictures, one can then say quite a lot about what the models imply on the level of observed data. For example, rather than just saying that no classical explanation with causal structure (i) and (ii) can explain the data, one might ask how much (i) or (ii) has to be relaxed for such a model to explain the data. We show that this type of questions can in many cases be formulated as linear programs, which means that their answer can be computed efficiently using standard techniques. As a package, we think it looks like the framework could prove to be a very useful tool.

** Published paper:** https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.140403