mirror of
https://github.com/quantumjim/Quantum-Computation-course-Basel.git
synced 2025-11-24 09:24:31 +01:00
94 lines
2.6 KiB
Plaintext
94 lines
2.6 KiB
Plaintext
{
|
||
"cells": [
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 1,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"'\\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'"
|
||
]
|
||
},
|
||
"execution_count": 1,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"\"\"\"\n",
|
||
"For 2×2 and 2×3 systems, the Positive Partial Transpose (PPT) criterion is necessary and sufficient for separability.\n",
|
||
"\n",
|
||
"Exercises:\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",
|
||
"\"\"\""
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"p=1.0 min eig(ρ^T_B)=-5.000000e-01 ENTANGLED\n",
|
||
"p=0.8 min eig(ρ^T_B)=-3.500000e-01 ENTANGLED\n",
|
||
"p=0.6 min eig(ρ^T_B)=-2.000000e-01 ENTANGLED\n",
|
||
"p=0.4 min eig(ρ^T_B)=-5.000000e-02 ENTANGLED\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"from qiskit.quantum_info import Statevector, DensityMatrix\n",
|
||
"\n",
|
||
"phi = Statevector([1,0,0,1])/np.sqrt(2)\n",
|
||
"rho_pure = DensityMatrix(phi).data\n",
|
||
"I4 = np.eye(4)/4\n",
|
||
"\n",
|
||
"def isotropic(p):\n",
|
||
" # |Φ+> density matrix with simple depolarizing noise when p<1\n",
|
||
" return p*rho_pure + (1-p)*I4\n",
|
||
"\n",
|
||
"for p in [1.0, 0.8, 0.6, 0.4]:\n",
|
||
" rho = isotropic(p)\n",
|
||
" rho_pt = DensityMatrix.partial_transpose(DensityMatrix(rho), [1]).data\n",
|
||
" eig = np.linalg.eigvalsh(rho_pt)\n",
|
||
" print(f\"p={p} min eig(ρ^T_B)={eig.min(): .6e} {'ENTANGLED' if eig.min()< -1e-10 else 'PPT'}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": []
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": ".venv",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.12.8"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 2
|
||
}
|