The Failure of Simultaneous Quantum Typicality

arXiv:2609.25726 · quant-ph, math-ph, math.FA, math.MP · Submitted 2026-09-22 · Read on arXiv

quant-ph, math-ph, math.FA, math.MP

Submitted: 2026-09-22

Updated: 2026-09-22

Terminology

• Trace — 31× in this paper · explained in 2 episodes
• Hilbert Space — 8× in this paper · explained in 2 episodes
• Decoupling — 6× in this paper · explained in 2 episodes
• Fidelity — 6× in this paper · explained in 2 episodes
• Trace Distance — 6× in this paper · explained in 3 episodes
• Entanglement — 5× in this paper · explained in 4 episodes
• Distillation — 2× in this paper · explained in 2 episodes
• Entanglement Distillation — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Entanglement Entropy — 1× in this paper · explained in 2 episodes

Sources

• One-shot multi-sender decoupling and simultaneous decoding for the quantum MAC
• One-shot Multiparty State Merging
• Small eigenvalues of Toeplitz operators, Lebesgue envelopes and Mabuchi geometry
• A solution to two party typicality using representation theory of the symmetric group
• Fully smooth one shot multipartite covering and decoupling of quantum states via telescoping

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