Undetermined states: how to find them and their applications

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.

6 pages, no figure

References in corpus (6)

• Graph States for Quantum Secret Sharing
• Cryptanalysis of the Hillery-Buzek-Berthiaume quantum secret-sharing protocol
• Three-party pure quantum states are determined by two two-party reduced states
• Only n-Qubit Greenberger-Horne-Zeilinger States are Undetermined by their Reduced Density Matrices
• The Parts Determine the Whole except for n-Qubit Greenberger-Horne-Zeilinger States
• A genuine four-partite entangled state