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New bounds were established for generalized relative entropy contraction under mappings, suggesting improvements over existing theories.
New bounds are given on the contraction of certain generalized forms of the relative entropy of two positive semi-definite operators under completely positive mappings. In addition, several conjectures are presented, one of which would give a strengthening of strong subadditivity. As an application of these bounds in the classical discrete case, a new proof of 2-point logarithmic Sobolev inequalities is presented in an Appendix.
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Mary Beth Ruskai (1994) studied this question.
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