对称信息完备正算子值测度与量子力学的概率表示
量子物理
2010-09-16 v2 数学物理
math.MP
摘要
在量子力学的概率表示框架内研究了对称信息完备正算子值测度(SIC-POVMs)。证明了SIC-POVM是概率表示的一个特例。SIC-POVM的存在性问题用与星积量子化方案相关的算子符号来表述。我们表明，SIC-POVMs（如果存在的话）必须遵循星积的一般规则，并由此推导出SIC投影算子的新关系。详细讨论了量子比特的情况，特别是建立了SIC概率表示与其他概率表示之间的关系，讨论了与互无偏基的联系，并给出了关于SIC-POVMs李代数结构的评注。
引用
@article{arxiv.1005.4091,
title = {Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics},
author = {S. N. Filippov and V. I. Man'ko},
journal= {arXiv preprint arXiv:1005.4091},
year = {2010}
}
备注
22 pages, 1 figure, LaTeX, partially presented at the Workshop "Nonlinearity and Coherence in Classical and Quantum Systems" held at the University "Federico II" in Naples, Italy on December 4, 2009 in honor of Prof. Margarita A. Man'ko in connection with her 70th birthday, minor misprints are corrected in the second version