Metric-Adjusted Skew Information: Convexity and Restricted Forms of Superadditivity

Cai, Liang; Hansen, Frank

doi:10.1007/s11005-010-0396-2

Cited by 21 publications

(25 citation statements)

References 27 publications

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“…To show the application of the measure (12) in the detection of nonlocality, we need a lemma of the strict convexity of the function (t−1) 2 f (t) . The convexity of the function (t−1) 2 f (t) has been well discussed (see [3,8]). However the strictness of the convexity has not been clarified as far as I know.…”

Section: Detection Of Nonlocality and Entanglement With Q Fmentioning

confidence: 99%

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Quantum uncertainty based on metric adjusted skew information

Cai

2018

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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Prompted by the open questions in Gibilisco [Int. J. Software Informatics, 8(3-4): 265, 2014], in which he introduced a family of measurement-induced quantum uncertainty measures via metric adjusted skew informations, we investigate these measures' fundamental properties (including basis independence and spectral representation), and illustrate their applications to detect quantum nonlocality and entanglement.Key words and phrases: metric adjusted skew information; operator monotone functions; quantum uncertainty; quantum nonlocality; quantum entanglement MSC2010 classification: 94A17, 81P15, 15A45.

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Section: Detection Of Nonlocality and Entanglement With Q Fmentioning

confidence: 99%

“…L ρ and R ρ are the positive definite commuting left and right multiplication operators by ρ. The metric adjusted skew information has the following interesting properties (see [3,4,8]). (c) The metric adjusted skew information decreases when several states are mixed:…”

Section: Introductionmentioning

confidence: 99%

Quantum uncertainty based on metric adjusted skew information

Cai

2018

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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“…Meantime, it is sufficient for the subadditivity that the bipartite state is pure. Other sufficient conditions for subadditivity of the Wigner-Yanase entropy are obtained in [8].…”

Section: Definitions and Notationmentioning

confidence: 99%

Bounds of the Pinsker and Fannes Types on the Tsallis Relative Entropy

Rastegin

2013

Math Phys Anal Geom

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Pinsker's and Fannes' type bounds on the Tsallis relative entropy are derived. The monotonicity property of the quantum f -divergence is used for its estimating from below. For order α ∈ (0, 1), a family of lower bounds of Pinsker type is obtained. For α > 1 and the commutative case, upper continuity bounds on the relative entropy in terms of the minimal probability in its second argument are derived. Both the lower and upper bounds presented are reformulated for the case of Rényi's entropies. The Fano inequality is extended to Tsallis' entropies for all α > 0. The deduced bounds on the Tsallis conditional entropy are used for obtaining inequalities of Fannes' type.

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“…This observation was extended in [9] to the paremeter range −1 ≤ p ≤ 2. Furthermore, the WYD skew information was recently generalized by Hansen [14] as follows: Let f be an operator monotone function on (0, ∞) such that f is symmetric (i.e., f (x) = f (x −1 )x for all x > 0) with f (1) = 1 and is regular in the sense that f (0) (:= lim xց0 f (x)) > 0.…”

Section: Quantum Skew Information and Quantum χ 2 -Divergencementioning

confidence: 62%

“…Quasi-entropies and monotone metrics are among the most important quantities in quantum information and quantum information geometry. More recent quantum quantities such as the quantum covariance in [29], the metric adjusted skew information (generalizing the WYD skew information) in [14,9] and the quantum χ 2divergence in [32,15] can be reformulated by quasi-entropies (see Subsection 1.4 and [21]).…”

Section: Introductionmentioning

confidence: 99%

Convexity of quasi-entropy type functions: Lieb's and Ando's convexity theorems revisited

Hiai

Petz

2013

Journal of Mathematical Physics

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Given a positive function f on (0, ∞) and a non-zero real parameter θ, we consider a functionin three matrices A, B > 0 and X. In the literature θ = ±1 has been typical. The concept unifies various quantum information quantities such as quasi-entropy, monotone metrics, etc. We characterize joint convexity/concavity and monotonicity properties of the function I θ f , thus unifying some known results for various quantum quantities.

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Metric-Adjusted Skew Information: Convexity and Restricted Forms of Superadditivity

Cited by 21 publications

References 27 publications

Quantum uncertainty based on metric adjusted skew information

Quantum uncertainty based on metric adjusted skew information

Bounds of the Pinsker and Fannes Types on the Tsallis Relative Entropy

Convexity of quasi-entropy type functions: Lieb's and Ando's convexity theorems revisited

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