Sub- and super-fidelity as bounds for quantum fidelity

TitleSub- and super-fidelity as bounds for quantum fidelity
Publication TypeJournal Article
Year of Publication2009
AuthorsMiszczak J.A., Puchała Z, Horodecki P, Uhlmann A., Życzkowski K
JournalQuantum Information & Computation
Date Published1
AbstractWe derive several bounds on fidelity between quantum states. In particular we show that fidelity is bounded from above by a simple to compute quantity we call super–fidelity. It is analogous to another quantity called sub–fidelity. For any two states of a two–dimensional quantum system ($N=2$) all three quantities coincide. We demonstrate that sub– and super–fidelity are concave functions. We also show that super–fidelity is super–multiplicative while sub–fidelity is sub–multiplicative and design feasible schemes to measure these quantities in an experiment. Super–fidelity can be used to define a distance between quantum states. With respect to this metric the set of quantum states forms a part of a $N^2-1$ dimensional hypersphere.