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Since the beginning of Information Theory, people have been interested in the limitations of communication and information. These limitations are completely characterized for two or three parties by Shannon inequalities: Strong subadditivity and monotonicity. However, with four or more parties it turns out there are infinitely many (!) relevant non-Shannon type inequalities, called Zhang-Yeung inequalities. The origin of these inequalities is still poorly understood. In the quantum case, Shannon inequalities are replaced by Von Neumann inequalities, but the question is whether there are indeed also non Von Neumann inequalities. I will talk about such inequalities for specific quantum states and their implications for (quantum) causal structures. These causal structures are a relatively recent development in the area of causal inference. The use of quantum Zhang-Yeung type inequalities might further specify the difference between certain quantum causal structures.

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Laurens Ligthart, QuSoft, Amsterdam
Seminar Room 0.02, ETP
Contact: David Gross