# Simplicial Sets and No-Go Theorems

- 14:00 28th January 2011 ( week 2, Hilary Term 2011 )Lecture Theatre B, Computing Laboratory

Simplicial sets are a combinatorial way of describing topological

spaces. We describe a simplicial set of the space of measurements and a

simplicial set of the space of possible outcomes of the measurements. An

experiment is then a map of simplicial sets from the space of outcomes to

the space of measurements. Basically, an outcome goes to the measurement

that corresponds to it. Global sections of such a map are actual results of

the experiment. By looking at different types of such maps, we formulate

different types of quantum systems and no-go theorems. One of the benefits

of this point of view is that the notion of compatibility (which restricts

the space of measurements) and entanglement (which restricts the space of

outcomes) are seen as intimately related phenomena.