Quantum Physics

In this talk, I will outline the current state of the art in the study of the reality of the quantum state.  The main theme will be that, although you cannot derive the reality of the quantum state in an ontological model without additional assumptions, you can place constraints on the amount of overlap between probability measures that begin to make psi-epistemic theories look implausible.  These overlap bounds come from noncontextuality inequalities, and there are two types in the literature: those based on Cabello-Severini-Winter type inequalities and those based on Yu-Oh type inequalities.  The latter type of overlap bound was not originally derived from noncontextuality, but thinking of them this way yields a new proof of the Yu-Oh inequality and gives rise to family of related inequalities.  I will also explain why I think that most papers on ovelap bounds (including my own) have adopted sub-optimal measures, introduce better ones, and explain how this affects the choice of the best experimental protocol for demonstrating overlap bounds.  

Collisions and modular variables; More on superoscillations and conservation of energy;  Time-Symmetric Quantum Mechanics and Free Will

The ideas of no-signalling, nonlocality, Bell inequalities, and quantum correlations can all be understood as implications of a presumed causal structure. In particular, the causal structure of the Bell scenario implies the Bell inequalities whenever the shared resource is presumed to act like a classical hidden random variable. If the shared resource in the scenario is a quantum system, however, then the quantum causal structure can give rise to a larger set of correlations, including probability distributions which violate Bell inequalities up to Tsirelson's bound. It is hard to generically distinguish between the classical and quantum correlations, though, because the standard method for computing Bell inequalities cannot be generalized to general causal scenarios. We therefore introduce a method (the "Inflation DAG" technique) to heuristically constrain the set of correlations compatible with a given classical causal structure, and we demonstrate how it may be used to derive explicit inequalities in terms of probabilities. We also discuss deriving physics-independent constraints, i.e. non-trivial inequalities which are nevertheless satisfied even by all quantum correlations, thereby quantifying some absolute limits as to what the universe allows.

[Unpublished results of E.W., Rob Spekkens, Tobias Fritz]

The Aharonov-Bergmann-Lebowitz Rule for weak and strong Measurements; The Quantum Pigeonhole Effect; Superoscillations and conservation of energy;  Conservation of energy and tunneling between space-like separated points.