PhD Thesis Defence

Monday, July 16, 2018 12:00 pm - 12:00 pm EDT (GMT -04:00)

Jitendra Prakash, Pure Mathematics, University of Waterloo

"Tsirelson's problems and entanglement breaking rank"

This talk will have two parts. In the first part, we consider a bipartite system with two observers, Alice and Bob, who are performing measurements in their labs. There are two models of quantum mechanics which describe the joint lab of Alice and Bob - the quantum model and the commuting quantum model. Tsirelson's original question asked whether these two models were essentially the same. We show that these two models are different for bipartite systems with five quantum experiments and binary outcomes for each experiment, by using the notion of correlation functions of graphs. 
In the second part, we introduce the notion of entanglement breaking rank of an entanglement breaking map. We show that computing the entanglement breaking rank of the entanglement breaking map defined by $$X \mapsto \frac{1}{d+1}(X+\mathrm{Tr}(X)),$$ where $X\in M_d(\mathbb C)$ is equivalent to the existence problem of SIC POVM in dimension $d$.