Almost One Bit Violation of Minimum-Output R'enyi Entropy Additivity Simultaneously at All Orders

arXiv:2609.18747 · quant-ph, math.OA · Submitted 2026-09-16 · Read on arXiv

quant-ph, math.OA

Submitted: 2026-09-16

Updated: 2026-09-16

Comments: 34 pages, 1 figure

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Additivity — 23× in this paper
• Trace — 6× in this paper · explained in 2 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Superadditivity — 2× in this paper · explained in 2 episodes
• Entanglement — 1× in this paper · explained in 4 episodes
• Large Language Model (LLM) — 1× in this paper · explained in 3 episodes

Sources

• Norm of matrix-valued polynomials in random unitaries and permutations
• Constructive counterexamples to the additivity of minimum output R'enyi entropy of quantum channels for all $p>1$
• More examples of additivity violation of the regularized minimum output entropy in the commuting-operator setup
• Counterexamples to additivity of minimum output p-R'enyi entropy of quantum channels for all p 0

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