On the 'Polarized distances between quantum states and observables'
D. A. Trifonov
Abstract
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 = D02 (1 - g(a,b)), which includes the known Bures-Uhlmann and Hilbert-Schmidt distances between quantum states, is established.
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