Year: 2025
Type: article
Abstract: We investigate global locations of Schmidt number witnesses which are outside of the convex set of all bipartite states. Their locations are classified by interiors of faces of the convex set of all states, by considering the line segments from them to the maximally mixed state. In this way, a nonpositive Hermitian matrix of trace 1 is located outside of one and only one face. Faces of the convex set of all states are classified by subspaces, which are range spaces of states belonging to specific faces. For a given subspace, we show that there exist Schmidt number $k+1$ witnesses outside of the face arising from this subspace if and only if every vector in the orthogonal complement of the subspace has Schmidt rank greater than $k$. Once we have Schmidt number $k+1$ witnesses outside of a face, we also have Schmidt number $2,3,\ensuremath{\cdots},k$ witnesses outside of the face.
Source: Physical Review A
DOI: 10.1103/bl7f-45vy
Authors: Kyung Hoon Han, Seung-Hyeok Kye
Institutions: University of Suwon, Seoul National University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414258666