55 lines
2.1 KiB
Python
55 lines
2.1 KiB
Python
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"""
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03_dps_level2_demo.py
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Demonstrates the level-2 DPS SDP (via dps_hierarchy.build_dps_problem) on
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two test states:
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A) the qutrit Werner state -- sanity check. PPT is already exactly
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tight for this family (p_c=1/4, see 02_werner_qutrit_symbolic.py), so
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DPS-2 cannot improve on it; well away from the boundary both should
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agree.
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B) the Tiles UPB bound-entangled state -- the interesting case. Plain
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PPT is blind (min eigenvalue ~0, "PPT to machine precision" as noted
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in the paper's own Tiles example), but DPS level 2 correctly detects
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the entanglement.
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Expected runtime: well under a minute with SCS.
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"""
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import cvxpy as cp
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from common import RHO_TILES, werner_qutrit, plain_ppt_feasible, plain_ppt_min_eig
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from dps_hierarchy import build_dps_problem, dps_feasible
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SOLVER = cp.SCS # swap to cp.MOSEK if you have a license -- likely much faster
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prob, rho_param, sigma = build_dps_problem(d=3, k=2)
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print(f"DPS level-2 SDP built: sigma shape {sigma.shape}\n")
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print("=" * 70)
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print("Sanity check: qutrit Werner state (known exact threshold p=1/4)")
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print("=" * 70)
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for p in [0.20, 0.40]:
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rho = werner_qutrit(p)
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ppt_ok = plain_ppt_feasible(rho)
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eig = plain_ppt_min_eig(rho)
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ok = dps_feasible(prob, rho_param, rho, solver=SOLVER, eps=1e-6)
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print(f"p={p:.2f}: PPT feasible={ppt_ok} (min eig {eig:+.5f}) "
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f"DPS-2 feasible={ok}")
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print("\n" + "=" * 70)
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print("Tiles UPB bound-entangled state (the interesting case)")
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print("=" * 70)
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ppt_ok = plain_ppt_feasible(RHO_TILES)
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eig = plain_ppt_min_eig(RHO_TILES)
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print(f"Plain PPT feasible: {ppt_ok} (min eigenvalue: {eig:.10f})")
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ok = dps_feasible(prob, rho_param, RHO_TILES, solver=SOLVER, eps=1e-6)
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print(f"DPS level-2 feasible: {ok} "
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f"({'NOT detected' if ok else 'ENTANGLEMENT DETECTED'})")
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print("\nRobustness across solver tolerances (guards against SDP numerical "
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"artifacts near a threshold -- see the chat for a case where this "
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"mattered):")
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for eps in [1e-5, 1e-6, 1e-7, 1e-8]:
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dps_feasible(prob, rho_param, RHO_TILES, solver=SOLVER, eps=eps, max_iters=50000)
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print(f" eps={eps}: status={prob.status}")
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