Characterizations of matrix and operator-valued Φ-entropies, and operator Efron–Stein inequalities
نویسندگان
چکیده
منابع مشابه
Characterisations of Matrix and Operator-Valued $Φ$-Entropies, and Operator Efron-Stein Inequalities
We derive new characterizations of the matrix Φ-entropy functionals introduced in Chen & Tropp (Chen, Tropp 2014 Electron. J. Prob.19, 1-30. (doi:10.1214/ejp.v19-2964)). These characterizations help us to better understand the properties of matrix Φ-entropies, and are a powerful tool for establishing matrix concentration inequalities for random matrices. Then, we propose an operator-valued gene...
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The most general type of measurement in quantum physics is modeled by a positive operator-valued measure (POVM). Mathematically, a POVM is a generalization of a measure, whose values are not real numbers, but positive operators on a Hilbert space. POVMs can equivalently be viewed as maps between effect algebras or as maps between algebras for the Giry monad. We will show that this equivalence i...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 2016
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.2015.0563