Results 241 to 250 of about 25,145 (258)
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2021
Let f be a convex function on (0, ∞), not necessarily operator convex unless we specify that. We use the convention in ( 2.2). Let M be a general von Neumann algebra. A measurement \(\mathcal {M}\) in M is given by \(\mathcal {M}=(A_j)_{1\le j\le n}\) for some \(n\in \mathbb {N}\), where Aj ∈ M+ for 1 ≤ j ≤ n and \(\sum _{j=1}^nA_j=1\). The measurement
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Let f be a convex function on (0, ∞), not necessarily operator convex unless we specify that. We use the convention in ( 2.2). Let M be a general von Neumann algebra. A measurement \(\mathcal {M}\) in M is given by \(\mathcal {M}=(A_j)_{1\le j\le n}\) for some \(n\in \mathbb {N}\), where Aj ∈ M+ for 1 ≤ j ≤ n and \(\sum _{j=1}^nA_j=1\). The measurement
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On f-divergence for $$\sigma $$-$$\oplus $$-measures
Soft Computing, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Agahi, Hamzeh, Yadollahzadeh, Milad
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2021
Let M be a general von Neumann algebra, and \(M_*^+\) be the positive cone of the predual M∗ consisting of normal positive linear functionals on M. Basics of von Neumann algebras are given in Sect. A.1.
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Let M be a general von Neumann algebra, and \(M_*^+\) be the positive cone of the predual M∗ consisting of normal positive linear functionals on M. Basics of von Neumann algebras are given in Sect. A.1.
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Annals of the Institute of Statistical Mathematics, 1991
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2021
Let M be a von Neumann algebra with its standard form \((M,\mathcal {H},J,\mathcal {P})\) as before. Throughout this chapter, we assume that f is an operator convex function on (0, ∞).
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Let M be a von Neumann algebra with its standard form \((M,\mathcal {H},J,\mathcal {P})\) as before. Throughout this chapter, we assume that f is an operator convex function on (0, ∞).
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Comparison of Contraction Coefficients for f-Divergences
Problems of Information Transmission, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Makur, A., Zheng, L.
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Relationships between certain f -divergences
2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2019We investigate the concavity deficit of the entropy functional. Some properties of the skew-divergence are developed and a “skew” $\chi^{2}$ divergence is introduced. Various relationships between these f - divergences and others are established, including a reverse Pinsker type inequality for the skew divergence, which in turn yields a sharpening on ...
James Melbourne +2 more
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Preservation of Maximal f-Divergences
2021In this chapter we will characterize the preservation of \(\widehat S_f\) under a unital normal positive map γ, i.e., the equality case in the monotonicity inequality \(\widehat S_f(\psi \circ \gamma \|\varphi \circ \varphi )\le \widehat S_f(\psi \|\varphi )\).
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Unitary orbit optimization of quantum f-divergence
Quantum Information ProcessingzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Haojian, Yan, Xiaojing
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Risk-Based Generalizations of f-divergences
2011We derive a generalized notion of f-divergences, called (f,l)-divergences. We show that this generalization enjoys many of the nice properties of f-divergences, although it is a richer family. It also provides alternative definitions of standard divergences in terms of surrogate risks.
García-García, Darío +2 more
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