Citation: Uhlmann, Armin. "The “transition probability” in the state space of a *-algebra." Reports on Mathematical Physics 9.2 (1976): 273-279.
Web: https://www.sciencedirect.com/science/article/pii/0034487776900604
Tags: Mathematical, Foundational, Subfactors, Operator-algebras, Information-theory
This is the paper where Uhlmann introduced a (generalized) version of the notion of fidelity of quantum states, and proved his now eponymous theorem. His definition works for more general *-algebras context, and is based on earlier *-algebraic work, namely
> Bures, Donald. "An extension of Kakutani's theorem on infinite product measures to the tensor product of semifinite w*-algebras." Transactions of the American Mathematical Society 135 (1969): 199-212.
The notion of fidelity was then lifted from this paper and brought into a much more concrete form in a paper by Jozsa, where the term fidelity was introduced:
> Jozsa, Richard. "Fidelity for mixed quantum states." Journal of modern optics 41.12 (1994): 2315-2323.
It is certainly interesting to see all of the early foundational ideas at play in this paper.