Sub–and super–fidelity as bounds for quantum fidelity

...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...

...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...

...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...

...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...

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