Schmidt Operator Norms and Entanglement Theory

We discuss the family of operator norms recently investigated in and some of their implications in quantum information. We referred to these norms as Schmidt norms since they derive from the Schmidt decomposition theorem for quantum states.These norms find applications to central problems in quantum information, including the problem of determining k-positivity of linear maps and entanglement witnesses, and finding bound entangled non-positive partial transpose states.