@article {iitisid_0421, title = {Sub- and super-fidelity as bounds for quantum fidelity}, journal = {Quantum Information \& Computation}, volume = {9}, number = {1\&2}, year = {2009}, note = {arXiv:0805.2037 IF=2.980(209); IF5=2.402(2010);}, month = {1}, pages = {0103{\textendash}0130}, abstract = {We 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{\textendash}fidelity. It is analogous to another quantity called sub{\textendash}fidelity. For any two states of a two{\textendash}dimensional quantum system ($N=2$) all three quantities coincide. We demonstrate that sub{\textendash} and super{\textendash}fidelity are concave functions. We also show that super{\textendash}fidelity is super{\textendash}multiplicative while sub{\textendash}fidelity is sub{\textendash}multiplicative and design feasible schemes to measure these quantities in an experiment. Super{\textendash}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.}, issn = {1533-7146}, author = {J.A. Miszczak and Zbigniew Pucha{\l}a and Pawe{\l} Horodecki and A. Uhlmann and Karol {\.Z}yczkowski} }