Optimal entanglement criteria from trace invariants

arXiv:2609.29471 · quant-ph · Submitted 2026-09-24 · Read on arXiv

quant-ph

Submitted: 2026-09-24

Updated: 2026-09-24

Terminology

• Trace — 110× in this paper · explained in 2 episodes
• Entanglement — 84× in this paper · explained in 3 episodes
• Embeddings — 8× in this paper · explained in 2 episodes
• Multipartite Entanglement — 4× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Interpretability — 1× in this paper · explained in 15 episodes
• Provenance — 1× in this paper · explained in 3 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes
• Semidefinite Program (SDP) — 1× in this paper · explained in 2 episodes

Sources

• Tensor invariants for multipartite entanglement classification
• Any-dimensional Positivstellens\"atze for symmetric functions
• Complete entanglement detection using polynomial invariants
• Detecting entanglement from few partial transpose moments and their decay via weight enumerators
• Tensor free probability theory: asymptotic tensor freeness and central limit theorem
• An introduction to graphical tensor notation for mechanistic interpretability

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