We determine the exact contraction coefficient (SDPI constant) of the quantum Jensen–Shannon divergence (QJSD) for the d-dimensional depolarizing channel Δₚ (ρ) = (1−p) ρ + (p/d) I. For all d ≥ 2 and p ∈ 0, 1, we obtain the closed form ηQJSD (Δₚ) = (1−p) ² / s, where s = 1 − (d−2) p/d, via a fully analytic argument based on the Bogoliubov–Kubo–Mori (BKM) metric, with no numerical verification.
Alex B. Shvets (Thu,) studied this question.