Added entanglement lecture applications notebooks

extra_resources/Entanglement_extra/7_Separability.ipynb

@@ -0,0 +1,93 @@
+{
+ "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
+}