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Super Quantum Measures on Finite Spaces

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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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Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Yongjian Xie & Fang Ren

  2. College of Science, Xi’an University of Science and Technology, Xi’an, 710054, China

    Aili Yang

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  1. Yongjian Xie
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  2. Aili Yang
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  3. Fang Ren
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Correspondence to Yongjian Xie.

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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

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