{
  "id": "tl-diagonal-postselection",
  "source_ids": [
    "zylberman-et-al-2025-diagonal",
    "zylberman-debbasch-2024-walsh"
  ],
  "statement": "A diagonal block applied to a specified input yields a conditional normalized state with success ||D psi||^2/alpha^2. Space/depth/accuracy tradeoffs must be compared at matched input, error and success contracts.",
  "lean_decl": [],
  "lean_status": "obligation",
  "used_by": [
    "spw-diagonal",
    "spw-walsh",
    "spw-envelope",
    "spw-fault-tolerant"
  ],
  "dependencies": [
    "family:matrix-contract",
    "family:state-action",
    "family:charged-access",
    "family:walsh-diagonal-phase"
  ],
  "next_action": "Prove the generic projected-branch probability identity using existing finite-matrix objects; keep the paper's literal dilation and circuit schedule as subsequent source obligations.",
  "tags": [
    "diagonal",
    "postselection",
    "success-cost",
    "planned-formalization"
  ],
  "failure_modes": [
    "Quoting per-attempt depth as time to a successful prepared state.",
    "Confusing state infidelity with vector or operator norm error, or forgetting alpha_total when converting source Eq. (18) normalized-block error to the local unscaled-operator convention.",
    "Ignoring input-state preparation, reflections or inverse access in amplification.",
    "Claiming a deterministic system-only non-unitary gate.",
    "Calling a uniform-input cost bound a bound for every localized input.",
    "Promoting the source Fig. 4 / Eqs. (19)-(21) / Appendix B signal sector before reconciling its labels.",
    "Assuming III.2 integer rounding and VIII.1 size versus depth accounting have already been reconciled."
  ]
}