Two variables functionals and inequalities related to measurable operators

Shao, Jingjing

doi:10.1186/s13660-017-1583-9

Cited by 3 publications

(3 citation statements)

References 22 publications

(39 reference statements)

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“…is jointly log-convex on (0, ∞)×(−∞, ∞) for any positive linear maps Λ on positive semi-definite matrices. We remark that for von Neumann algebras similar results have been studied by Shao [111]. In particular, our inequality for conditional expectation can also be derived from [111,Corollary 3.13] via an averaging trick.…”

Section: Complex Interpolation and Noncommutative L P Spacessupporting

confidence: 67%

“…We remark that for von Neumann algebras similar results have been studied by Shao [111]. In particular, our inequality for conditional expectation can also be derived from [111,Corollary 3.13] via an averaging trick.…”

Section: Complex Interpolation and Noncommutative L P Spacessupporting

confidence: 67%

“…is a product state and can be viewed as a c-q channel applied on the sequence as described in Eq. (111). For the case of i.i.d.…”

Section: Applications Of Auxiliary Functions In Error Exponent Analysismentioning

confidence: 99%

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Properties of Scaled Noncommutative Rényi and Augustin Information

Cheng

Gao

Hsieh

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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The scaled Rényi information plays a significant role in evaluating the performance of information processing tasks by virtue of its connection to the error exponent analysis. In quantum information theory, there are three generalizations of the classical Rényi divergence-the Petz's, sandwiched, and log-Euclidean versions, that possess meaningful operational interpretation. However, these scaled noncommutative Rényi informations are much less explored compared with their classical counterpart, and lacking crucial properties hinders applications of these quantities to refined performance analysis. The goal of this paper is thus to analyze fundamental properties of scaled Rényi information from a noncommutative measure-theoretic perspective. Firstly, we prove the uniform equicontinuity for all three quantum versions of Rényi information, hence it yields the joint continuity of these quantities in the orders and priors. Secondly, we establish the concavity in the region of s ∈ (−1, 0) for both Petz's and the sandwiched versions. This completes the open questions raised by Holevo [IEEE Trans. Inf. Theory, 46(6):2256-2261, 2000], Mosonyi and Ogawa [Commun. Math. Phys, 355 (1): 2017]. For the applications, we show that the strong converse exponent in classical-quantum channel coding satisfies a minimax identity. The established concavity is further employed to prove an entropic duality between classical data compression with quantum side information and classical-quantum channel coding, and a Fenchel duality in joint source-channel coding with quantum side information in the forthcoming papers.

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Section: Complex Interpolation and Noncommutative L P Spacessupporting

confidence: 67%

Section: Complex Interpolation and Noncommutative L P Spacessupporting

confidence: 67%

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Properties of Scaled Noncommutative Rényi and Augustin Information

Cheng

Gao

Hsieh

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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Properties of Noncommutative Rényi and Augustin Information

Cheng

Gao

Hsieh

2022

Commun. Math. Phys.

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New inequalities for (p,h)-convex functions for τ-measurable operators

Ighachane,

Bouchangour

2023

Filomat

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The main goal of this article is to present new inequalities for (p, h)-convex and (p,h) log-convex functions for a non-negative super-multiplicative and super-additive function h. Our first main result will be h? (v/?) ? (h(1 ? v) f (a) + h(v) f (b))? ? f ? [((1 ? v)ap + vbp) 1 p] / (h(1 ? ?) f (a) + h(?) f (b))? ? f ? [((1 ? ?)ap + ?bp)1p] ? h? (1 ? v/1 ? ?), for the positive (p, h)-convex function f, when ? ? 1, p ? R\{0} and 0 ? v ? ? ? 1. This gives a generalization of an important result due to M. Sababheh [Linear Algebra Appl. 506 (2016), 588-602]. As applications of our results, we present many inequalities for the trace, and the symmetric norms for ?-measurable operators.

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Two variables functionals and inequalities related to measurable operators

Cited by 3 publications

References 22 publications

Properties of Scaled Noncommutative Rényi and Augustin Information

Properties of Scaled Noncommutative Rényi and Augustin Information

Properties of Noncommutative Rényi and Augustin Information

New inequalities for (p,h)-convex functions for τ-measurable operators

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