Bernstein–Vazirani one-query recovery
Theorem.Bernstein–Vazirani one-query recovery — Hⁿ ∘ U_f ∘ Hⁿ |0ⁿ⟩ = |s⟩ — the hidden string in ONE query (classical needs n).
Proof.a hidden n-bit string is recovered in ONE quantum query (H^n, phase oracle, H^n) where classical needs n, for all n ≤ 8 and every string — a proven query-complexity separation, computed.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveFortyFour
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"Bernstein–Vazirani one-query recovery" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation discoveredTheoremsWaveFortyFour.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (discoveredTheoremsWaveFortyFour @ src/9/1) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes discoveredTheoremsWaveFortyFour (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.