One-way puzzles exist if and only if proper quantum distribution learning is average-case hard, and PP ≠ BQP if and only if agnostic quantum distribution learning with KL divergence is hard.
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Hardness of Quantum Distribution Learning and Quantum Cryptography
One-way puzzles exist if and only if proper quantum distribution learning is average-case hard, and PP ≠ BQP if and only if agnostic quantum distribution learning with KL divergence is hard.