mirror of
https://github.com/quantumjim/Quantum-Computation-course-Basel.git
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94 lines
2.6 KiB
Plaintext
94 lines
2.6 KiB
Plaintext
{
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"'\\nFor 2×2 and 2×3 systems, the Positive Partial Transpose (PPT) criterion is necessary and sufficient for separability.\\n\\nExercises:\\n- Extend to a 2×3 example by padding qubits or adding a qutrit toy model with dims=(2,3).\\n- Wrap into a helper function `is_entangled_ppt(rho, dims)`.\\n'"
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"\"\"\"\n",
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"For 2×2 and 2×3 systems, the Positive Partial Transpose (PPT) criterion is necessary and sufficient for separability.\n",
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"\n",
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"Exercises:\n",
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"- Extend to a 2×3 example by padding qubits or adding a qutrit toy model with dims=(2,3).\n",
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"- Wrap into a helper function `is_entangled_ppt(rho, dims)`.\n",
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"\"\"\""
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]
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},
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"text": [
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"p=1.0 min eig(ρ^T_B)=-5.000000e-01 ENTANGLED\n",
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"p=0.8 min eig(ρ^T_B)=-3.500000e-01 ENTANGLED\n",
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"p=0.6 min eig(ρ^T_B)=-2.000000e-01 ENTANGLED\n",
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"p=0.4 min eig(ρ^T_B)=-5.000000e-02 ENTANGLED\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"from qiskit.quantum_info import Statevector, DensityMatrix\n",
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"\n",
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"phi = Statevector([1,0,0,1])/np.sqrt(2)\n",
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"rho_pure = DensityMatrix(phi).data\n",
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"I4 = np.eye(4)/4\n",
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"\n",
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"def isotropic(p):\n",
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" # |Φ+> density matrix with simple depolarizing noise when p<1\n",
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" return p*rho_pure + (1-p)*I4\n",
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"\n",
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"for p in [1.0, 0.8, 0.6, 0.4]:\n",
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" rho = isotropic(p)\n",
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" rho_pt = DensityMatrix.partial_transpose(DensityMatrix(rho), [1]).data\n",
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" eig = np.linalg.eigvalsh(rho_pt)\n",
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" print(f\"p={p} min eig(ρ^T_B)={eig.min(): .6e} {'ENTANGLED' if eig.min()< -1e-10 else 'PPT'}\")"
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]
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