Applications of a family of norms in entanglement theory

I will introduce a family of operator norms based on the Schmidt decomposition theorem and focus on their applications in quantum information theory. We will discuss two problems in particular: the existence problem for non-positive partial transpose bound entangled states and the problem of computing or estimating the minimum gate fidelity of a quantum channel. We will discuss some techniques for computing the norms and how they apply in the special cases of NPPT bound entanglement and minimum gate fidelity.