2026/07/16 by Debbie Leung, Benjamin Lovitz, Peixue Wu
#quant-ph #math-ph #math.MP #math.PR
Additivity of minimum output entropies is a central problem in quantum information theory. Nonadditivity is known for every Rényi order p>1, at the von Neumann point p=1, and near p=0, while most of the interval 0<p<1 has remained open. We prove that for every Rényi order p satisfying either p>3/4 or 0≤ p<1/4, there exist finite-dimensional projection-induced quantum channels such that additivity of the minimum output p-Rényi entropy fails. The proof combines two correlated random-projection constructions: a product-conjugate Bell-state witness for p>3/4, and a transpose-complement rank-defect witness for p<1/4. Thus the unresolved part of 0<p<1 is reduced to [1/4,3/4]. Our estimates also improve the output dimension threshold for additivity violation of minimum output von Neumann entropy, first established in Belinschi, Collins and Nechida.