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arXiv · 0805.2037

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

J. A. Miszczak·Z. Puchała·P. Horodecki·A. Uhlmann·K. Życzkowski
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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.

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J. A. Miszczak, Z. Puchała, P. Horodecki, A. Uhlmann, K. Życzkowski. 2008-11-19. Sub-- and super--fidelity as bounds for quantum fidelity. https://arxiv.org/abs/0805.2037

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