On the notion of causal influence

Paolo Perinotti, University of Pavia, Italy

We address the question whether a reversible transformation produces a causal influence from one of its input systems to one of its outputs. In quantum theory the causal influence relation is typically identified with signalling. There is also a second notion borrowed from the theory of quantum cellular automata, and we adopt an extension of the latter definition in the context of general operational probabilistic theories. We show that in the quantum case our notion coincides with signalling. We will also discuss classical theory, where the two notions are different. Following the proof of equivalence in the quantum case, we identify general conditions under which causal influence coincides with signalling. We will illustrate, in particular, the property of "no interaction without disturbance". We conclude illustrating an algebraic construction that turns out particularly useful for the purpose of analysing causal influence relations.

Recording of the talk