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Subadditivity of Matrix phi-Entropy and Concentration of Random Matrices
Matrix concentration inequalities provide a direct way to bound the typical
spectral norm of a random matrix. The methods for establishing these results
often parallel classical arguments, such as the Laplace transform method. This
work develops a matrix extension of the entropy method, and it applies these
ideas to obtain some matrix concentration inequalities.Comment: 23 page
Perturbation 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 systems. The result turns out to be a practical way of the expansion
calculation of von Neumann entropy.Comment: 7 page
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