55 lines
2.4 KiB
Python
55 lines
2.4 KiB
Python
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"""
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DIAGNOSTIC: run a single SDP step seeded with the EXACT optimal dual witnesses of the
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known-good point rho_mix = 0.5*(Bell_AB x Bell_CD) + 0.5*(Bell_AC x Bell_BD), which is a
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manifestly valid PPT-mixture state (explicit convex combination of two product states)
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scoring EXACTLY (3.0, 3.0, 3.0) for (||M_AB||_*, ||M_AC||_*, ||M_AD||_*).
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Since rho_mix is feasible and, for these SPECIFIC witnesses O_S = U_S V_S^T (from its own
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SVD), achieves t = sum_S tr(O_S^T M_S(rho_mix)) = 3.0 exactly, any correct implementation
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of
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max_{rho in PPT-mixtures} min_S tr(O_S^T M_S(rho))
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MUST return an optimal value >= 3.0 (the SDP maximizes over a set containing rho_mix).
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If the reported optimal t comes back < 3.0 here, that is conclusive evidence of an
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implementation bug in the SDP construction itself (not just a weakness of the alternating
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heuristic / random restarts).
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Run this BEFORE re-running the full alternating_search -- it isolates the problem.
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"""
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import numpy as np
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from sdp_ppt_mixture import solve_fixed_witness_step, true_norms_and_witnesses, CLUSTERS
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data = np.load('O_seed.npz')
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O = {name: data[name] for name, _, _ in CLUSTERS}
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print("Loaded seed witnesses (each should have operator norm 1):")
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for name, Om in O.items():
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print(f" ||O_{name}||_op =", np.linalg.norm(Om, ord=2))
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print()
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print("Solving ONE SDP step with these witnesses...")
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rho_val, t_val, M_vals = solve_fixed_witness_step(O, verbose=True)
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print()
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print("SDP optimal t =", t_val)
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print("Expected: t >= 3.0 (since rho_mix itself is feasible and scores exactly 3.0 here)")
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print()
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norms, _ = true_norms_and_witnesses(M_vals)
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print("True nuclear norms of the returned optimal rho:", norms)
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if t_val < 2.99:
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print()
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print("!!! t < 3.0 -- there IS an implementation bug in the SDP construction. !!!")
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print("Next diagnostic step: check prob.status, and manually verify PSD/PPT of")
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print("rho_val's 7 constituent blocks (may need to re-solve while keeping rho_gammas")
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print("accessible, i.e. return them from solve_fixed_witness_step for inspection).")
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else:
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print()
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print("t >= 3.0 as expected: the SDP construction is correct.")
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print("The earlier runs' convergence to 7/3 was the alternating heuristic getting")
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print("stuck in a (large-basin) symmetric fixed point from random starts -- not a bug.")
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print("Fix: warm-start alternating_search from these O_seed witnesses (or from a small")
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print("random perturbation of them) instead of purely random O's.")
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