Static classical-quantum-entanglement trade-offs: an entropic converse and single-letter characterizations

arXiv:2609.23298 · quant-ph, cs.IT, math.IT · Submitted 2026-09-20 · Read on arXiv

quant-ph, cs.IT, math.IT

Submitted: 2026-09-20

Updated: 2026-09-20

Comments: 81 pages, 5 figures

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

Terminology

• Entanglement — 71× in this paper · explained in 3 episodes
• Additivity — 43× in this paper · explained in 1 episode
• Trace — 19× in this paper · explained in 2 episodes
• Regularization — 16× in this paper · explained in 3 episodes
• Trace Distance — 7× in this paper · explained in 3 episodes
• Distillation — 5× in this paper · explained in 2 episodes
• Superadditivity — 5× in this paper · explained in 2 episodes
• Verification — 4× in this paper · explained in 2 episodes
• Entanglement Distillation — 2× in this paper · explained in 2 episodes
• Entanglement Entropy — 2× in this paper · explained in 2 episodes
• AI Agents — 1× in this paper · explained in 2 episodes
• Additivity Condition — 1× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Core — 1× in this paper · explained in 2 episodes
• Decode — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Resource Constraints — 1× in this paper · explained in 3 episodes

Sources

• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Concentrating Partial Entanglement by Local Operations
• Trade-off capacities of the quantum Hadamard channels
• A Resource Framework for Quantum Shannon Theory
• Convexity and Operational Interpretation of the Quantum Information Bottleneck Function
• Distillation of secret key and entanglement from quantum states
• The exact cost of redistributing multipartite quantum states
• Entropic proofs of Singleton bounds for quantum error-correcting codes
• Complete entropic inequalities for quantum Markov chains
• General Entanglement Breaking Channels
• Trading classical communication, quantum communication, and entanglement in quantum Shannon theory
• Efficient algorithms for quantum information bottleneck
• Properties of Conjugate Channels with Applications to Additivity and Multiplicativity
• Quantum logarithmic Sobolev inequalities and rapid mixing
• Useful states and entanglement distillation
• Singleton Bounds for Entanglement-Assisted Classical and Quantum Error Correcting Codes
• Capacities of Quantum Amplifier Channels
• A semidefinite program for distillable entanglement
• Peres-Horodecki separability criterion for continuous variable systems

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• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians