Quantum divergences with p-power means

Lam, Nguyen; Le, Phi

doi:10.1016/j.laa.2020.09.009

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Cited by 6 publications

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“…is the unique solution of the corresponding least square problem. In another paper [12] Lam and Le introduced and studied quantum divergences with ppower means µ p (t, A, B). Notice that one of the most important things in the least square problem is the uniqueness of the solution.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The matrix Heinz mean and related divergence

Dinh

Le²,

et al. 2022

Hacettepe Journal of Mathematics and Statistics

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In this paper, we introduce a new quantum divergencewhere 0 < α < 1. We study the least square problem with respect to this divergence. We also show that the new quantum divergence satisfies the Data Processing Inequality in quantum information theory. In addition, we show that the matrix p-power mean µ p (t, A, B) = ((1 − t)A p + tB p ) 1/p satisfies the in-betweenness property with respect to the new divergence.

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Section: Introductionmentioning

confidence: 99%

“…Finally, we also show that the matrix power mean µ p (t, A, B) satisfies the in-betweenness property (Theorem 3.2). On the in-betweenness property we refer the readers to [2,[4][5][6][7][8][9]12].…”

Section: Introductionmentioning

confidence: 99%