A Short Tour of the Laws of Entanglement (And How to Evade Them)

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Constructs a family of embezzling states with Schmidt coefficients ~1/√j (normalization ~log n) that let two separated parties convert a product target into an entangled target by local unitaries with fidelity at least 1 − (log m)/log n, so achieving error ε requires n ~ (1/ε)×(target size) (polynomial blowup). Multiparty embezzlement exists but costs doubly exponential resources. Tools: explicit Schmidt permutations, correlated‑sampling robustness, and uses in quantum games and the quantum reverse Shannon theorem; the schemes work only approximately and require large dimensions.

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1. 0:00Introduction
2. 0:52Structure
3. 1:48The Great Laws Part 1
4. 2:40What is embezzlement
5. 3:06Perfect embezzlement
6. 10:26How to embezzle
7. 13:53Permutation matrices
8. 16:33Further developments
9. 20:53Entanglement in the Hilbert Space
10. 25:53Twoplayer games
11. 27:44Quantum games
12. 33:30Quantum reversion theorem
13. 35:29The first application of embezzlement
14. 37:43Monogamy
15. 39:45Entanglement Measures
16. 43:26Entanglement Definition
17. 45:23Conclusion