Ali Kavruk, Virginia Commonwealth University
"Christandl's Problem and Connes' Embedding Problem"
In Quantum Information Theory Peres-Horodecki-Woronowicz's PPT (positive partial transpose) criterion is an effective method to identify separable states if the local dimensions are low ((2,2), (2,3) or (3,2)). M. Christandl then asks if bi-PPT cones can identify separable states on a quantum system with arbitrary local dimensions. Applicability in Quantum Entanglement we present general theory of symmetrization in the operator system category. We go through the stability properties of these functors under quotients, duality, tensor products, etc. We then express Christandl's Problem in this setting. We will see that this problem is connected with Connes' Embedding Problem and give various open problems which are implied by these two questions. This will be an introductory talk and accessible to grad students.
MC 5417