Undetermined states: how to find them and their applications

TL;DR

This paper explores undetermined states in quantum information, proposing methods to identify them through stabilizer codes and graph states, and demonstrates their application in secure quantum secret sharing.

Contribution

It introduces novel approaches to find undetermined quantum states using stabilizer codes and graph state local complementation, with applications in quantum security.

Findings

Established a relation between stabilizer codewords and undetermined states.

Studied local complementation rules of graph states.

Applied undetermined states to secure quantum secret sharing.

Abstract

We investigate the undetermined sets consisting of two-level, multi-partite pure quantum states, whose reduced density matrices give absolutely no information of their original states. Two approached of finding these quantum states are proposed. One is to establish the relation between codewords of the stabilizer quantum error correction codes (SQECCs) and the undetermined states. The other is to study the local complementation rules of the graph states. As an application, the undetermined states can be exploited in the quantum secret sharing scheme. The security is guaranteed by their undetermineness.