关于“量子态与观测量的极化距离”
On the 'Polarized distances between quantum states and observables'
摘要：
修正了在前一篇论文quant-ph/0005087，v.1（参考文献1）中提出的距离构造方案。文献1中命题1的表述并不保证三角不等式成立，因此文献1中的某些泛函D（a，b）实际上是拟距离。在本文中，我们给出了（平方）形式D（a，b）^2 = f（a）^2 + f（b）^2 - 2f（a）f（b）g（a，b）的泛函D（a，b）是距离的充分条件，并给出了这类距离的一些例子.建立了一个单参数推广的有界距离D（a，b）^2 = D_0^2（1 - g（a，b）），它包含了已知的量子态之间的Bures-Uhlmann距离和Hilbert-Schmidt距离.
英文摘要：
The scheme for construction of distances, presented in the previous paper quant-ph/0005087, v.1 (Ref. 1) is amended. The formulation of Proposition 1 of Ref. 1 does not ensure the triangle inequality, therefore some of the functionals D(a,b) in Ref. 1 are in fact quasi-distances. In this note we formulate sufficient conditions for a functional D(a,b) of the (squared) form D(a,b)^2 = f(a)^2 + f(b)^2 - 2f(a)f(b)g(a,b) to be a distance and provide some examples of such distances. A one parameter generalization of a bounded distance of the (squared) form D(a,b)^2 = D_0^2 (1 - g(a,b)), which includes the known Bures-Uhlmann and Hilbert-Schmidt distances between quantum states, is established.
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