Young Researchers Conference - 2006

In stochastic treatments of the ERRB set-up, it is equivalent to impose Bell\'s inequalities, a local causality condition, or a certain \"non-contextual hidden variables\" condition. But these conditions are violated by quantum mechanics. On the other hand, it is possible to view quantum mechanics as part of \"quantum measure theory\", a generalization of probability measure theory that allows pair wise interferences between histories whilst banning higher order interference. In this setting, is may be possible find quantum analogues of the three stochastic conditions. Following this line of inquiry, we will see that quantum measure theory allows no stronger violations of Bell\'s inequalities than does standard quantum theory. We also gain some insights into how to define causality in quantum theory.

Inferring a quantum system\'s state, from repeated measurements, is critical for verifying theories and designing quantum hardware. It\'s also surprisingly easy to do wrong, as illustrated by maximum likelihood estimation (MLE), the current state of the art. I\'ll explain why MLE yields unreliable and rank-deficient estimates, why you shouldn\'t be a quantum frequentist, and why we need a different approach. I\'ll show how operational divergences -- well-motivated metrics designed to evaluate estimates -- follow from quantum strictly proper scoring rules. This motivates Bayesian Mean Estimation (BME), and I\'ll show how it fixes most of the problems with MLE. I\'ll conclude with a couple of speculations about the future of quantum state and process estimatio