Quantum Nonlocality and Contextuality
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. Similarly, quantum observables exhibit the phenomenon of contextuality, which means that their actual values must necessarily depend on the particular choice of measurement that is performed to uncover them.
In this course, I will first give a short introduction into these two concepts. Then I will turn to the 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.
Then the question arises what distinguishes quantum correlations from more general non-signalling correlations, and more generally, "why" physics behaves according to the probabilistic rules of Hilbert space quantum theory. I will show some examples of simple operational principles (discovered by people from quantum information theory) that give partial answers to these questions, and also experiments that are currently performed to rule out possible beyond-quantum physics.
This is not a course on interpretations of quantum mechanics! The focus is on mathematical physics, concrete theorems, and (if time permits) possible applications such as device-independent cryptography.