Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Quantum probability is a natural generalization of standard probability. Any one random variable is exactly as it was before, but random variables no longer have to commute. Remarkably, quantum probability is empirically true, in the same sense that classical probability is true in science. We simply do not usually see it, because most of our affairs lie within a commutative realm of the non-commutative reality.

Quantum probability is also an unavoidable generalization: it cannot exist within classical probability. One rigorous version of this conclusion is that quantum probability violates Bell-type inequalities. However, traditional Bell-type protocols, which are also called non-locality demonstrations, are statistically inefficient. They consume many quantum bits of data for each bit of persuasion. In this talk I will describe some new protocols that are more efficient. I will also discuss upper bounds on how efficient any such protocol can be, and related questions.