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Quantum System
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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
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Sub–and super–fidelity as bounds for quantum fidelity
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Citations: 10
)
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J. A Miszczak
,
Z. Puchała
,
P. Horodecki
,
A. Uhlmann
,
K. Zyczkowski
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 superfidelity. It is analogous to another quantity called subfidelity. For any two states of a twodimensional
quantum system
(N=2) all three quantities coincide. We demonstrate that sub and superfidelity are concave functions. We also show that superfidelity is supermultiplicative while subfidelity is submultiplicative and design feasible schemes to measure these quantities in an experiment. Superfidelity 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 $N^21$ dimensional hypersphere.
Published in 2009.
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Citation Context
(5)
...So, the subfidelity [
10
] and the superfidelity [10,11] have been proposed as those measures that are easier to compute...
...So, the subfidelity [10] and the superfidelity [
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 Puchała
,
et 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 subfidelity [
12
] and the superfidelity [12,13] have been studied...
...Recently, the subfidelity [12] and the superfidelity [
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 Augusiakand
,
et al.
Towards measurable bounds on entanglement measures
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Citations
(10)
Bounds on Shannon distinguishability in terms of partitioned measures
(
Citations: 3
)
Alexey E. Rastegin
Journal:
Quantum Information Processing  QUANTUM INF PROCESS
, vol. 10, no. 1, pp. 123138, 2011
Experimentally feasible measures of distance between quantum operations
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)
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Transition Probability (Fidelity) and Its Relatives
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Partitioned trace distances
(
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