Unbounded Holevo additivity gaps in finite dimensions

arXiv:2609.18222 · quant-ph, cs.IT, math-ph, math.IT, math.MP · Submitted 2026-09-16 · Read on arXiv

quant-ph, cs.IT, math-ph, math.IT, math.MP

Submitted: 2026-09-16

Updated: 2026-10-05

Terminology

• Additivity — 33× in this paper · explained in 1 episode
• Trace — 11× in this paper · explained in 2 episodes
• Entanglement — 5× in this paper · explained in 3 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Superadditivity — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Verification — 2× in this paper · explained in 2 episodes
• Graph Construction — 1× in this paper · explained in 3 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes

Sources

• On some additivity problems in quantum information theory
• Non-additivity of Renyi entropy and Dvoretzky's Theorem
• Hastings' additivity counterexample via Dvoretzky's theorem
• Norm of matrix-valued polynomials in random unitaries and permutations
• Laws of large numbers for eigenvectors and eigenvalues associated to random subspaces in a tensor product
• Almost one bit violation for the additivity of the minimum output entropy
• On Hastings' counterexamples to the minimum output entropy additivity conjecture
• Towards a state minimizing the output entropy of a tensor product of random quantum channels
• Counterexamples to additivity of minimum output p-Renyi entropy for p close to 0
• The strong asymptotic freeness of Haar and deterministic matrices
• Random quantum channels I: graphical calculus and the Bell state phenomenon
• Random quantum channels II: Entanglement of random subspaces, Renyi entropy estimates and additivity problems
• Random matrix techniques in quantum information theory
• Haagerup's inequality and additivity violation of the Minimum Output Entropy
• Constructive counterexamples to the additivity of minimum output R'enyi entropy of quantum channels for all $p>1$
• Entanglement of random subspaces via the Hastings bound
• Comments on Hastings' Additivity Counterexamples
• Asymptotically well-behaved input states do not violate additivity for conjugate pairs of random quantum channels
• Additivity rates and PPT property for random quantum channels
• Revisiting additivity violation of quantum channels

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