Quantum 4

on YouTube ↗56m

" summary

Quantum commitments and many other primitives can plausibly exist without one-way functions: oracle separations show pseudorandom state implies commitments and that quantum commitments exist relative to quantum or classical oracles even if BQP = QMA or P = NP, respectively. Constructions go from quantum one-way states to one-way puzzle -> commitments by converting many-state copies into classical shadows and proving inversion remains hard. A separate line reduces average-case hardness of output probabilities (permanent / boson sampling / random circuits) to one-way puzzles. Open: base commitments on weaker worst-case assumptions (e.g., P ≠ PSPACE).

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" chapters (8)

1. 0:00Quantum cryptography assumptions
2. 2:33Quantum key distribution
3. 4:01Pseudorandom states in quantum
4. 16:50Quantum cryptographic primitives
5. 23:31One-way state generators
6. 37:49One-way puzzles in quantum
7. 43:48Building puzzles from quantum advantage
8. 53:14Open problems in quantum crypto

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