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A true quantum signature algorithm based on continuous-variable entanglement state is proposed. In the suggested algorithm, a key-pair, i.e. private signature key and public verification key, is generated based on a one-way function. By employing the signature key, a message state is encoded into a 2k-particle entangled state and a two-particle entangled state is prepared. The resulting states are exploited as a signature of the message state. The signature can be decoded under the verification key when it needs to be verified. Subsequently, a decoded message state and a two-particle entangled state are obtained. To compare the decoded states and the original states, a quantum circuit for comparing these states is exploited. Making use of measurement results of the quantum circuit one can judge the authenticity of the received signature. According to the security requirement of the signature scheme, the suggested algorithm has been proven to be theoretically secure by using the Shannon information theory.

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The perovskite phase in PZN-PMN-PT pseudoternary ceramics was stabilized by the addition of excess constituent divalent oxides (PbO, MgO, and ZnO). 5 mol % excess MgO or 7.5 mol % excess PbO was sufficient to eliminate the remnant cubic pyrochlore phase after sintering at 1100 C C for 1 h. The enhanced diffuse phase transition (DPT) and the decrease in the electrical resistivity were observed in the presence of excess ZnO or MgO. These were interpreted in terms of the additional formation of negatively charged, short-range ordered 1:1 domains with a concomitant generation of charge carriers (holes). The behavior of excess MgO or ZnO at concentrations above 5 mol % was studied by examining complex impedance patterns.