Abstract
In this paper, the properties of the super quantum measures are studied. Firstly, the products of Dirac measures are discussed; Secondly, based on the properties of Dirac measures, the structures of super quantum measures are characterized; At last, we prove that any super quantum measure can determine a unique diagonally positive strongly symmetric signed measure. This result verifies the conjecture which was proposed by Gudder.
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Acknowledgements
This work is partially supported by National Science Foundation of China (Grant No. 11201279, 11271237, 61273311) and the Fundamental Research Funds for the Central Universities (Grant No. GK201002037, GK201302054).
The first author is indebted to helpful communications with Professor Gudder. We also thank the anonymous referees for the very thorough reading and contributions to improve our presentation of the paper.
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Xie, Y., Yang, A. & Ren, F. Super Quantum Measures on Finite Spaces. Found Phys 43, 1039–1065 (2013). https://doi.org/10.1007/s10701-013-9731-7
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DOI: https://doi.org/10.1007/s10701-013-9731-7