44 lines
1.5 KiB
Python
44 lines
1.5 KiB
Python
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"""compute_seed_witnesses.py -- computes and saves the exact optimal dual witnesses
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O_AB, O_AC, O_AD (each with operator norm 1) for the known-good state
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rho_mix = 0.5 * (Bell_AB x Bell_CD) + 0.5 * (Bell_AC x Bell_BD)
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which is a manifestly valid PPT-mixture state (explicit convex combination of two
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product states) scoring EXACTLY (3.0, 3.0, 3.0) for
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(||M_AB||_*, ||M_AC||_*, ||M_AD||_*) -- see mixture_search.py for the derivation.
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Run this once to produce O_seed.npz, which diagnostic_seeded_run.py and
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seeded_exploration.py both load.
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"""
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import numpy as np
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from cluster import cluster_map, nuc
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from mixture_search import bellpair_state, full_tensor_mixed_fast
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CLUSTERS = [('AB', 0, 1), ('AC', 0, 2), ('AD', 0, 3)]
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def true_norms_and_witnesses(M_vals):
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norms, O_opt = {}, {}
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for name, M in M_vals.items():
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U, s, Vt = np.linalg.svd(M)
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norms[name] = s.sum()
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O_opt[name] = U @ Vt
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return norms, O_opt
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if __name__ == "__main__":
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psi1 = bellpair_state(((0, 1), (2, 3)))
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psi2 = bellpair_state(((0, 2), (1, 3)))
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rho_mix = 0.5 * np.outer(psi1, np.conj(psi1)) + 0.5 * np.outer(psi2, np.conj(psi2))
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C = full_tensor_mixed_fast(rho_mix)
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M_vals = {name: cluster_map(C, s0, s1) for name, s0, s1 in CLUSTERS}
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norms, O_seed = true_norms_and_witnesses(M_vals)
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print('norms at rho_mix:', norms, ' (expect all == 3.0)')
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for k, v in O_seed.items():
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print(f' operator norm of O_seed[{k}] =', np.linalg.norm(v, ord=2), '(should be 1.0)')
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np.savez('O_seed.npz', **O_seed)
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print('Saved O_seed.npz')
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