A fibre bundle over manifolds of quantum channels and its application to quantum statistics

By A. Fujiwara, Hiroshi Imai. 2008

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Quantum limits in optical interferometry (2014, unknown): “Based on the mathematical analysis of the geometry of quantum channels (Fujiwara and Imai, 2008; 4 Matsumoto, 2010) general frameworks have been developed allowing to find fundamental bounds on quantum precision enhancement for general decoherence models (Demkowicz-Dobrzański et al., 2012; Escher…”
Quantum metrology with nonclassical states of atomic ensembles (2016, background): “The maximum of the quantum Fisher information over all possible probe states is bounded as (Fujiwara and Imai, 2008) max ρ̂0 FQ [ Λ⊗Nθ (ρ̂0) ] ≤ 4 min {K̂`} { N‖αK‖+N(N−1)‖βK‖2 } , (115) where αK = ∑ `(∂θK̂ † ` )(∂θK̂`), βK = i ∑ `(∂θK̂ † ` )K̂`, ‖·‖ denotes the operator norm, and the minimization…”
General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology (2011, background): “Ĥ (m) 2 = 0 implies δx ∼ 1/ √ N was derived for the more restrict situation of finite-dimensional spaces in [26], wh ich”
Macroscopic quantum states: Measures, fragility, and implementations (2017, background): “34 Demkowicz-Dobrzanski et al. (2012); Escher et al. (2011); Fujiwara and Imai (2008); Sekatski et al. (2016) 35 A. Lopez Incera et al., in preparation.”