منابع مشابه
Von Neumann entropy and majorization
We consider the properties of the Shannon entropy for two probability distributions which stand in the relationship of majorization. Then we give a generalization of a theorem due to Uhlmann, extending it to infinite dimensional Hilbert spaces. Finally we show that for any quantum channel Φ, one has S(Φ(ρ)) = S(ρ) for all quantum states ρ if and only if there exists an isometric operator V such...
متن کاملFractal Von Neumann Entropy
We consider the fractal von Neumann entropy associated with the fractal distribution function and we obtain for some universal classes h of fractons their entropies. We obtain also for each of these classes a fractal-deformed Heisenberg algebra. This one takes into account the braid group structure of these objects which live in two-dimensional multiply connected space. PACS numbers: 05.30.-d; ...
متن کاملPreprint Series 2012 / 2013 No : 11 Title : ‘ Von Neumann Entropy and Majorization ’ Author ( S )
In this paper, we firstly consider the properties of the Shannon entropy for two probability distributions which stand in the relationship of majorization. Then we give a generalized Uhlmann theorem in an infinite dimension Hilbert space. Also, we show that S(Φ(ρ)) = S(ρ) for all quantum states ρ if and only if there exists an isometry operator V such that Φ(ρ) = V ρV , where Φ is a quantum cha...
متن کاملKernel Integration using von Neumann Entropy
Kernel methods provide a computational framework to integrate heterogeneous biological data from different sources for a wide range of learning algorithms by designing a kernel for each different information source and combining them in a unique kernel through simple mathematical operations. We develop here a novel technique for weighting kernels based on their von Neumann entropy. This permits...
متن کاملPerturbation theory of von Neumann Entropy
In quantum information theory, von Neumann entropy plays an important role. The entropies can be obtained analytically only for a few states. In continuous variable system, even evaluating entropy numerically is not an easy task since the dimension is infinite. We develop the perturbation theory systematically for calculating von Neumann entropy of non-degenerate systems as well as degenerate s...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2013
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2013.06.019