2014/08/15 by Keiji Matsumoto, Matsumoto, Keiji
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Advanced Thermodynamics and Statistical Mechanics
paper · pdf · doi:10.48550/arxiv.1408.3462
We study tree kinds of quantum fidelity. Usual Uhlmann's fidelity, minus of f-divergence when f(x)=-√(x), and the one introduced by the author via reverse test. All of them are quantum extensions of classical fidelity, where the first one is the largest and the third one is the smallest. We characterize them in terms of convex optimization, and introduce their 'dual' quantity, or the polar of the minus of the fidelity. They turned out to be monotone increasing by unital completely positive maps, concave, and linked to its classical version via optimization about classical-to-quantum maps and quantum-to-classical maps.