Families of $k$-positive maps and Schmidt number witnesses from generalized equiangular measurements

Abstract

Quantum entanglement is an important resource in many modern technologies, like quantum computation or quantum communication and information processing. Therefore, most interest is given to detect and quantify entangled states. Entanglement degree of bipartite mixed quantum states can be quantified using the Schmidt number. Witnesses of the Schmidt numbers are closely related to $k$-positive linear maps, for which there is no general construction. Here, we use the generalized equiangular measurements to define a family of $k$-positive maps and the corresponding Schmidt number witnesses.