"""
04_tiles_noise_scan.py

Noise-robustness comparison: find the critical white-noise fraction p_c at
which each criterion stops detecting entanglement of

    rho(p) = p * rho_Tiles + (1-p) * I/9

Reproduces (see the chat for the full discussion/derivation):
  - plain shadow-map / de Vicente Bloch-representation criterion:
        p_c ~ 0.9493  (tolerance ~5.07%)
  - DPS level 2:
        p_c ~ 0.951   (tolerance ~4.9%)

i.e. DPS level 2 barely improves on the much cheaper order-1 correlation
criterion for THIS state -- see 05_local_filtering.py for the much bigger
lever (local filtering).

Expected runtime: seconds for the shadow-map part; a few minutes for the
DPS-2 bisection (12-16 SDP solves).
"""
import cvxpy as cp
from common import noisy_tiles, shadow_map_nuclear_norm
from dps_hierarchy import build_dps_problem, dps_feasible

SOLVER = cp.SCS

print("Shadow-map criterion threshold:")
lo, hi = 0.0, 1.0
for _ in range(40):
    mid = (lo + hi) / 2
    if shadow_map_nuclear_norm(noisy_tiles(mid)) > 1:
        hi = mid
    else:
        lo = mid
print(f"  p_c = {hi:.5f}  (tolerance {100 * (1 - hi):.2f}%)")

print("\nDPS level-2 threshold:")
prob, rho_param, sigma = build_dps_problem(d=3, k=2)
lo, hi = 0.0, 1.0
for i in range(16):
    mid = (lo + hi) / 2
    ok = dps_feasible(prob, rho_param, noisy_tiles(mid), solver=SOLVER,
                       eps=1e-7, warm_start=True)
    if ok:
        lo = mid
    else:
        hi = mid
    print(f"  [{i + 1}] p={mid:.5f}  feasible={ok}")
print(f"  p_c = {hi:.5f}  (tolerance {100 * (1 - hi):.2f}%)")