01193nas a2200181   4500000000100000008004100001260000600042100002200048700002200070700002100092700001500113700002200128245005900150300001600209490000600225520076600231022001400997       2009                            d  c11 aJaroslaw Miszczak1 aZbigniew Puchała1 aPaweł Horodecki1 aA. Uhlmann1 aKarol Życzkowski00aSub- and super-fidelity as bounds for quantum fidelity  a0103–01300 v93 aWe 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.  a1533-7146