| Some quantum error correction codewords are undetermined by their parts (2008) | |||||||||
Abstract | |||||||||
| We investigate the two-level, multi-partite quantum states with their non-injective reduced density matrices. As pointed out by Walck and Lyon, the undetermined states are stabilizer states \cite{4}. From this viewpoint, we firstly discuss the connections between the codewords of stabilizer quantum error correction codes and the undetermined states. Using these connections, some novel sets of undetermined states are found. Then we discuss the usefulness of undeterminedness property on quantum cryptography. In particular, we modify the quantum secret sharing scheme proposed by Hillery \emph{et. al. }\cite{3}. The security is proved using the undeterminedness of the Greenberger-Horne-Zeilinger (GHZ) states. Finally, the undetermined mixed states are also studied.. Comment: 9 pages, no figure | |||||||||
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