**A family of norms with applications in entanglement theory** - David Kribs

I will discuss recent work with Nathaniel Johnston in which we consider a family of operator norms that quantify the degree of entanglement in quantum states. The norms are defined by the Schmidt decomposition theorem for quantum states, and they can be used to tackle two fundamental problems in quantum information theory: the classification problem for k-positive linear maps and entanglement witnesses, and the existence problem for non-positive partial transpose bound entangled states. Time dependent, I'll discuss some properties of the norms and their applications.