Sub-- and super--fidelity as bounds for quantum fidelity

@misc{citeulike:2802476, 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--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.}, author = {Miszczak, J. A. and Pucha\&\#x142;a, Z. and Horodecki, P. and Uhlmann, A. and \&\#x17b;yczkowski, K. }, citeulike-article-id = {2802476}, eprint = {0805.2037}, keywords = {mathematics, physics, printed, quantum, quantum-information}, month = {May}, posted-at = {2008-05-15 19:53:57}, priority = {3}, title = {Sub\&\#45;\&\#45; and super\&\#45;\&\#45;fidelity as bounds for quantum fidelity}, url = {http://arxiv.org/abs/0805.2037}, year = {2008} }

TY - ELEC ID - citeulike:2802476 L3 - citeulike-article-id:2802476 TI - Sub-- and super--fidelity as bounds for quantum fidelity N2 - 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--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. KW - mathematics KW - physics KW - printed KW - quantum KW - quantum-information AU - Miszczak, JA AU - Puchała, Z AU - Horodecki, P AU - Uhlmann, A AU - Życzkowski, K PY - 2008/May/14/ UR - http://arxiv.org/abs/0805.2037 ER -