Title: Semidefinite programming representations for separable states
|Affiliation:||University of Cambridge|
|Zoom:||Please email Emma Watson|
The set of separable (i.e., non-entangled) bipartite states is a convex set that plays a fundamental role in quantum information theory. The problem of optimizing a linear function on the set of separable states is closely related to polynomial optimization on the sphere. After recalling the sum-of-squares hierarchy for this problem, I will show bounds on the rate of convergence of this SDP hierarchy; and prove that the set of separable states has no SDP representation of finite size. This shows that the set of separable states provides a counter-example to the Helton-Nie conjecture about semidefinite representations of convex semialgebraic sets.