51 lines
1.5 KiB
Python
51 lines
1.5 KiB
Python
|
"""
|
||
|
|
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}%)")
|