Sub- and super-fidelity as bounds for quantum fidelity

  • Authors:

  • Jarosław Adam Miszczak;Zbigniew Puchała;Paweł Horodecki;Armin Uhlmann;Karol Zyczkowski

  • Affiliations:

  • Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Gliwice, Poland;Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Gliwice, Poland;Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Gdańsk, Poland and National Quantum Information Centre of Gdańsk, Sopot, Poland;Institute of Theoretical Physics, University of Leipzig, Leipzig, Germany;Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagielloński, Kraków, Poland and Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Warszawa, Poland

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2009

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Abstract

We derive several bounds on fidelity between quantum states. In particular we show thatfidelity 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 demonstratethat sub- and super-fidelity are concave functions. We also show that super-fidelity issuper-multiplicative while sub-fidelity is sub-multiplicative and design feasible schemesto measure these quantities in an experiment. Super-fidelity can be used to define adistance between quantum states. With respect to this metric the set of quantum statesforms a part of a N2 - 1 dimensional hypersphere.