Conditioning on Subalgebras - Entropy Duality and Generalized Quantum Stein's Lemma in von Neumann Algebras

arXiv:2610.00772 · quant-ph, math-ph, math.MP, math.OA · Submitted 2026-09-30 · Read on arXiv

quant-ph, math-ph, math.MP, math.OA

Submitted: 2026-09-30

Updated: 2026-09-30

Comments: 67 pages, no figures

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

Terminology

• Trace — 37× in this paper · explained in 2 episodes
• Hilbert Space — 12× in this paper · explained in 2 episodes
• Fidelity — 8× in this paper · explained in 2 episodes
• Generalization — 8× in this paper · explained in 13 episodes
• Additivity — 5× in this paper · explained in 1 episode
• Entanglement — 5× in this paper · explained in 3 episodes
• Axioms — 4× in this paper · explained in 2 episodes
• Objective Function — 4× in this paper · explained in 2 episodes
• Core — 3× in this paper · explained in 2 episodes
• Homogeneity — 3× in this paper · explained in 2 episodes
• Adaptation — 2× in this paper · explained in 1 episode
• Decode — 1× in this paper · explained in 2 episodes
• Modularity — 1× in this paper · explained in 9 episodes
• Regularization — 1× in this paper · explained in 3 episodes

Sources

• On Bures distance over standard form vN-algebras
• The quantum capacity of channels with arbitrarily correlated noise
• Sandwiched R'enyi Divergence Satisfies Data Processing Inequality
• On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources
• A Generalization of Quantum Stein's Lemma
• Min- and Max- Relative Entropies and a New Entanglement Monotone
• Quantum reference frames, measurement schemes and the type of local algebras in quantum field theory
• Generalized quantum asymptotic equipartition
• Jones index, secret sharing and total quantum dimension
• Potential theoretic approach to rendezvous numbers
• Relative entropy for von Neumann subalgebras
• Distance measures to compare real and ideal quantum processes
• Generalized Stein's lemma and asymptotic equipartition property for subalgebra entropies
• Recoverability for optimized quantum $f$-divergences
• Concise lectures on selected topics of von Neumann algebras
• Generalized Quantum Stein's Lemma and Second Law of Quantum Resource Theories
• Multi-interval Subfactors and Modularity of Representations in Conformal Field Theory
• A solution of the generalised quantum Stein's lemma
• Entanglement in von Neumann Algebraic Quantum Information Theory
• A note on continuous entropy

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