The weak Ruskai-Audenaert conjecture holds for qutrit channels, and the strong form holds for all qubit-input channels, cq/qc channels, and a nonzero-measure set in every dimension.
Journal of Physics A: Mathematical and Theoretical , abstract =
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The Ruskai-Audenaert conjecture & equipartitions of positive operators
The weak Ruskai-Audenaert conjecture holds for qutrit channels, and the strong form holds for all qubit-input channels, cq/qc channels, and a nonzero-measure set in every dimension.