On the monotonicity of scalar curvature in classical and quantum information geometry
On the monotonicity of scalar curvature in classical and quantum information geometry
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DOI：
10.1063/1.1834693
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发表时间：
2005-02-01
影响因子：
1.3
通讯作者：
Isola, T
中科院分区：
文献类型：
--
作者：
Gibilisco, P;Isola, T
本文研究了概率向量单形上α-几何在混合标量曲率下的单调性。从所得结果和数值数据中，我们得到了关于量子α几何和Wigner-Yanase-Dyson信息的一些结果。最后，我们表明，这最后一个猜想意味着真理的Petz猜想的Bogoliubov-Kubo-Mori单调度量的标量曲率的单调性。(C)2005年美国物理学会。
We study the monotonicity under mixing of the scalar curvature for the alpha-geometries on the simplex of probability vectors. From the results obtained and from numerical data, we are led to some conjectures about quantum alpha-geometries and Wigner-Yanase-Dyson information. Finally, we show that this last conjecture implies the truth of the Petz conjecture about the monotonicity of the scalar curvature of the Bogoliubov-Kubo-Mori monotone metric. (C) 2005 American Institute of Physics.