Monotonicity of optimized quantum f-divergence

Abstract

Optimized quantum f-divergence was first introduced by Wilde in Wil18. Wilde raised the question of whether the monotonicity of optimized quantum f-divergence can be generalized to maps that are not quantum channels. We answer this question by generalizing the monotonicity of optimized quantum f-divergences to positive trace preserving maps satisfying a Schwarz inequality.

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