Quantum Nonlocality and General Probabilistic Theories
Abstract:
As shown theoretically by John Bell, and confirmed in numerous experiments, quantum theory admits "nonlocal" correlations which are impossible to achieve within classical physics. We will start by discussing how such Bell inequalities can be formulated mathematically, and how their violation in quantum physics enables certification of randomness, which has implications for fundamental physics as well as technology. Then we will turn to a surprising insight by Tsirelson and Popescu and Rohrlich: namely, that there are conceivable nonlocal correlations -- "PR-boxes" -- that violate Bell inequalities by more than any quantum state, while still respecting the "no-signalling principle" necessary to comply with relativity. This raises the question of "why" these superstrong correlations do not seem to be present in nature, or, more generally, why probabilities of detector clicks are described by the Hilbert space formalism of quantum theory. We will see how "probabilistic theories" more general than quantum theory can be formulated, and how some set of simple physical principles picks out quantum theory from the landscape of all probabilistic theories. This is comparable to the way in which Einstein's light postulate and relativity principle single out Minkowski space from the landscape of all geometries. If time permit, we will also briefly discuss experiments that are currently testing quantum theory against more general alternatives.
Remark. This is not a course on interpretations of quantum mechanics! The focus is on mathematical physics, concrete theorems, and possible applications in the context of quantum information theory.
Literature: Nice read to get an idea: S. Popescu, Nonlocality beyond quantum mechanics, Nature Physics 10, 264-270 (2014).