Constructing k-Schmidt witnesses for infinite-dimensional systems

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.

Keywords:

• k-Schmidt witness
• infinite dimension
• Schmidt number
• entanglement
• positive linear map

AMS Subject Classifications:

• 47L07
• 47A30
• 81P40

Notes

1 The research is supported in part by National Natural Science Foundation of China [grant number 11371279].