Fidelity, sub-fidelity, super-fidelity and their preservers
2015 ◽
Vol 13
(03)
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pp. 1550027
Keyword(s):
Sub- and super-fidelity describe respectively the lower and super bound of fidelity of quantum states. In this paper, we obtain several properties of sub- and super-fidelity for both finite- and infinite-dimensional quantum systems. Furthermore, let H be a separable complex Hilbert space and ϕ : 𝒮(H) → 𝒮(H) a map, where 𝒮(H) denotes the convex set of all states on H. We show that, if dim H < ∞, or, if dim H = ∞ and ϕ is surjective, then the following statements are equivalent: (1) ϕ preserves the super-fidelity; (2) ϕ preserves the fidelity; (3) ϕ preserves the sub-fidelity; (4) there exists a unitary or an anti-unitary operator U on H such that ϕ(ρ) = UρU† for all ρ ∈ 𝒮(H).
1969 ◽
Vol 21
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pp. 1421-1426
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2020 ◽
Vol 18
(08)
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pp. 2150003
1966 ◽
Vol 18
◽
pp. 897-900
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1974 ◽
Vol 26
(1)
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pp. 115-120
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2015 ◽
Vol 17
(05)
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pp. 1450042
2011 ◽
Vol 50
(1)
◽
pp. 63-78
Keyword(s):
2020 ◽
pp. 155-165
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Keyword(s):
1974 ◽
Vol 26
(1)
◽
pp. 247-250
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