**Comparison of experiments on general quantum systems - a Quantum
Blackwell Theorem** - Francesco Buscemi

Between 1949 and 1953, Blackwell proved a theorem, which is now a famous result in classical statistics, formalizing the idea that one experiment is more informative than another if and only if the latter can be simulated by suitably processing the outcomes of the former. A quantum analogue of Blackwell Theorem was proposed in [Shmaya, J.Math.Phys. 38, 9717-9727 (2005)]. Shmaya's comparison method, however, always and necessarily requires the presence of an extra entangled resource, even if the two experiments to be compared are purely classical. This makes Blackwell Theorem, which is a classical result,
independent from Shmaya's approach, which is, instead, purely quantum. Here, by introducing the notion of state space processing for general convex sets of states, we are able to bridge such a gap and treat classical and quantum experiments comparison on an equal footing. As an interesting by-product, we show that it is in fact possible to re-derive all of Shmaya's results without ever resorting to any extra entangled resource.