Abstract
We study the structure of k-Schmidt witnesses in infinite dimensions. We show that for any states with Schmidt number greater than , there exists a
-Schmidt witnesses of the form
to detect it, where
and
is a finite rank self-adjoint operator. We provide a method to construct
-Schmidt witnesses with these forms. An elementary operator criterion to determine the lower bound of the Schmidt number of a state is obtained. We also construct a class of 2-Schmidt witnesses, from which we can detect the entanglement of states by entries of their matrix representations.
Notes
1 The research is supported in part by National Natural Science Foundation of China [grant number 11371279].