A New Quantum f-Divergence for Trace Class Operators in Hilbert Spaces

Dragomir, Sever S

doi:10.3390/e16115853

Cited by 3 publications

(3 citation statements)

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“…A new version of quantum f -divergence. Referring to [5] in (1.1), we presented the definition of the divergence D f (• •) between invertible density operators. Obviously, we can define this quantity between positive definite operators as in (1.1).…”

Section: 3mentioning

confidence: 99%

“…In 1985, Petz introduced the general notion of quasientropy for the state space of a von Neumann algebra, and he considered the quantum f -divergence as a special case of the large class of quasientropies (for further details, see [22], [23] and the references therein). In 2014, a different concept of quantum f -divergence was introduced by Dragomir in [5] as…”

Section: Introductionmentioning

confidence: 99%

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Maps preserving a new version of quantum $f$ -divergence

Gaál¹

2017

Banach J. Math. Anal.

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For an arbitrary nonaffine operator convex function defined on the nonnegative real line and satisfying f (0) = 0, we characterize the bijective maps on the set of all positive definite operators preserving a new version of quantum f -divergence. We also determine the structure of all transformations leaving this quantity invariant on quantum states for any strictly convex functions with the properties f (0) = 0 and lim x→∞ f (x)/x = ∞. Finally, we derive the corresponding result concerning those transformations on the set of positive semidefinite operators. We emphasize that all the results are obtained for finite-dimensional Hilbert spaces.

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Section: 3mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Maps preserving a new version of quantum $f$ -divergence

Gaál¹

2017

Banach J. Math. Anal.

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“…There has been a considerable amount of research in this direction. These new divergences have been shown to be related to a wide range of fundamental concepts in quantum information theory, such as entanglement theory, quantum error correction, and quantum channel capacities [ 1 , 6 , 7 , 8 , 9 ]. In general terms, the approach employed in the related literature is to introduce functionals depending on a defining Csiszár function

defined over a set of operators.…”

Section: Introductionmentioning

confidence: 99%

Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences

Bussandri

Osán

2023

Entropy

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We introduce a new family of quantum distances based on symmetric Csiszár divergences, a class of distinguishability measures that encompass the main dissimilarity measures between probability distributions. We prove that these quantum distances can be obtained by optimizing over a set of quantum measurements followed by a purification process. Specifically, we address in the first place the case of distinguishing pure quantum states, solving an optimization of the symmetric Csiszár divergences over von Neumann measurements. In the second place, by making use of the concept of purification of quantum states, we arrive at a new set of distinguishability measures, which we call extended quantum Csiszár distances. In addition, as it has been demonstrated that a purification process can be physically implemented, the proposed distinguishability measures for quantum states could be endowed with an operational interpretation. Finally, by taking advantage of a well-known result for classical Csiszár divergences, we show how to build quantum Csiszár true distances. Thus, our main contribution is the development and analysis of a method for obtaining quantum distances satisfying the triangle inequality in the space of quantum states for Hilbert spaces of arbitrary dimension.

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Improvements of Jensen's inequality and its converse for strongly convex functions with applications to strongly f-divergences

Ivelić Bradanović

2024

Journal of Mathematical Analysis and Applications

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A New Quantum f-Divergence for Trace Class Operators in Hilbert Spaces

Abstract: A new quantum f -divergence for trace class operators in Hilbert Spaces is introduced. It is shown that for normalised convex functions it is nonnegative. Some upper bounds are provided. Applications for some classes of convex functions of interest are also given.

Cited by 3 publications

References 25 publications

Maps preserving a new version of quantum $f$ -divergence

Maps preserving a new version of quantum $f$ -divergence

Quantum Distance Measures Based upon Classical Symmetric Csiszár Divergences

Improvements of Jensen's inequality and its converse for strongly convex functions with applications to strongly f-divergences

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