Eur. Phys. J. D 61, 261-265 (2011)
https://doi.org/10.1140/epjd/e2010-10374-9

Undetermined states: how to find them and their applications

¹ ERATO-SORST Quantum Computation and Information Project, Japan Science and Technology Agency, 5-28-3, Hongo, Bunkyo-ku, Tokyo, Japan
² Department of Physics, Chung Yuan Christian University, 32023 Chungli, Taiwan

Corresponding author: ^a lyhsu@cycu.edu.tw

Received: 28 June 2010
Published online: 3 December 2010

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.