Unified framework demonstrates exact contraction coefficients for midpoint divergences under depolarizing channels, indicating strong data-processing inequalities.
A unified metric-transport framework for strong data-processing inequalities of midpoint divergences under depolarizing channels. We prove a universal exact contraction formula, establish sharp binary threshold and interior optimality, characterize the transport class boundary via Sturm-certified Jensen–Rényi obstructions, and provide complete SDPI analysis beyond the transport class. All claims fully proved.
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Alex Shvets (2026) studied this question.
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