QLunch: Structure from Non-Signalling
Title: Structure from Non-Signalling
In the 1960s, John Bell discovered that there is a classically observable difference between quantum physics and classical physics. For a long time, it was unclear whether this difference is as large as one could imagine based merely on a certain non-signalling principle deriving from special relativity. By the 1990s, however, this idea was excluded as results of Tsirelson, Popescu and Rohrlich implied a gap between the predictions of quantum physics and those of non-signalling. In this talk - which requires no knowledge of anything mentioned in the abstract - I will present a theorem show-casing a situation where the above-mentioned gap changes in a surprising fashion. This yields in particular a recharacterization of the (very complicated set of) “tensor-product quantum behaviours” as those behaviours admitting Stinespring dilations subject to non-signalling conditions. I will exhibit some curious corollaries of this recharacterization (mostly due to recent results of others), and also discuss how to make an approximate version of the theorem. Finally, if time permits, I will briefly discuss possible, and impossible, generalisations of the theorem.
It is helpful, but not necessary, to know about classical channels (= Markov kernels), quantum channels (= completely positive trace-preserving maps) and Stinespring’s dilation theorem. We will mostly need the finite-dimensional versions.