χ_R(∣CS⟩^⊗3) ≥ 3

CS orbit, two-qubit.

Participate

Run it yourself, or point a coding agent at it.

git clone https://github.com/unitaryfoundation/stabrank
cd stabrank
# describe your decomposition in bounds/mybound.json
make fit BOUND=bounds/mybound.json ARGS=--write
make verify BOUND=bounds/mybound.json

fit solves for the exact coefficients, or tells you no exact combination of your terms reproduces the target. verify rebuilds the identity in exact arithmetic. If it passes, open a pull request adding the file and the leaderboard picks it up on the next build.

A bound the pipeline cannot check is recorded as cited and never takes a record.

← back to the board

Verification

verified certificate script asserted: CERTIFIED chi(CS^3) >= 3, by an argument declared exact throughout (no floating-point margin)

Notes

χ(ψ ⊗ φ) ≥ χ(ψ) when φ has a nonzero computational amplitude: (I ⊗ ⟨00|) |CS⟩^⊗3 = |CS⟩^⊗2 / 2 and a computational-basis slice of a stabilizer state is a stabilizer state or zero, so a decomposition of |CS⟩^⊗3 slices to one of |CS⟩^⊗2 with no more terms, and χ(|CS⟩^⊗3) ≥ χ(|CS⟩^⊗2) = 3 by the exact rank-2 exclusion the same certificate runs. Exact throughout. The block slice-and-lift of cert_cs_m3_lift.py raises the bound to 4 at the reproduced tier (CS-m3-lower-4.json); this file keeps the verified-tier value.

Attribution

Vincent Russo · stabrank verify_challenge · projection monotonicity from the exact rank-2 exclusion at m = 2

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "CS",
  "m": 3,
  "direction": "lower",
  "rank": 3,
  "certificate": {
    "script": "verify_challenge/cert_cs_m2_rank2.py",
    "expect": "CERTIFIED chi(CS^3) >= 3",
    "exact": true
  },
  "provenance": {
    "author": "Vincent Russo",
    "reference": "stabrank verify_challenge",
    "method": "projection monotonicity from the exact rank-2 exclusion at m = 2",
    "date": "2026-10-21",
    "github": [
      "vprusso"
    ]
  },
  "notes": "chi(psi (x) phi) >= chi(psi) when phi has a nonzero computational amplitude: (I (x) <00|) |CS>^3 = |CS>^2 / 2 and a computational-basis slice of a stabilizer state is a stabilizer state or zero, so a decomposition of |CS>^3 slices to one of |CS>^2 with no more terms, and chi(|CS>^3) >= chi(|CS>^2) = 3 by the exact rank-2 exclusion the same certificate runs. Exact throughout. The block slice-and-lift of cert_cs_m3_lift.py raises the bound to 4 at the reproduced tier (CS-m3-lower-4.json); this file keeps the verified-tier value."
}