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Sub–and super–fidelity as bounds for quantum fidelity

Sub–and super–fidelity as bounds for quantum fidelity,J. A Miszczak,Z. Puchała,P. Horodecki,A. Uhlmann,K. Zyczkowski

Sub–and super–fidelity as bounds for quantum fidelity   (Citations: 10)
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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.
Published in 2009.
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    • ...So, the sub-fidelity [10] and the super-fidelity [10,11] have been proposed as those measures that are easier to compute...
    • ...So, the sub-fidelity [10] and the super-fidelity [10,11] have been proposed as those measures that are easier to compute...

    Alexey E. Rastegin. Bounds on Shannon distinguishability in terms of partitioned measures

    • ...The most interesting feature of the superfidelity is that it provides an upper bound for quantum fidelity [14]...
    • ...It was also shown that it can be used to define such metrics on MN [14 ]a s...
    • ...Itwas shown in Ref. [14] that quantities defined inEqs...

    Zbigniew Puchałaet al. Experimentally feasible measures of distance between quantum operation...

    • ...There are many other bounds, older [19] and newer ones, [22, 23]...

    Armin Uhlmann. Transition Probability (Fidelity) and Its Relatives

    • ...Recently, the sub-fidelity [12] and the super-fidelity [12,13] have been studied...
    • ...Recently, the sub-fidelity [12] and the super-fidelity [12,13] have been studied...

    Alexey E. Rastegin. Partitioned trace distances

    • ...In particular we concentrate on the bounds measurable on two copies of a state, i.e., those from Refs.[25,44,46],however,werecallalsotheresultof[43].Then,inSect.4weprovide yetanotherproofoftheMintert–Buchleitnerboundonconcurrence.Recentlyanalternative proof of the MB bound, based on the upper bound on Uhlmann–Jozsa fidelity [59,60]fromRef.[61],wasprovidedinRef.[62].Here,utilizingthenotionoftheconjugate function of concurrence, but also the ...
    • ...[55–57] to derive measurable bounds on the entanglement measures from mean values of quantum observables) and the very recent upper bound on the fidelity [59,60] proved by Miszczak et al. [61]...
    • ...We can utilize the aforementioned upper bound for the Ulhmann–Jozsa fidelity [59] defined as F(ρ1 ,ρ 2) = Tr � √ ρ1ρ2 √ ρ1. Namely, it was shown in Ref. [61] that the...
    • ...In the case of the reduction map R some steps towards optimization can be made using the bound on fidelity [61], as it is pointed out in the paper...

    Remigiusz Augusiakandet al. Towards measurable bounds on entanglement measures

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