Added entanglement lecture applications notebooks

extra_resources/Entanglement_extra/2_locc.ipynb

@@ -0,0 +1,73 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\"\"\"\n",
+    "LOCC cannot create entanglement. Simulate LOCC-like maps (local unitaries + classical randomness) on product states.\n",
+    "\n",
+    "Exercises:\n",
+    "- Add classical mixing over different local unitaries and show separability persists for mixed states.\n",
+    "\"\"\""
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Entangled after local? False\n",
+      "Entangled after RXX? True\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "from qiskit import QuantumCircuit\n",
+    "from qiskit.quantum_info import Statevector\n",
+    "\n",
+    "def entangled(psi):\n",
+    "    s = np.linalg.svd(psi.data.reshape(2,2), compute_uv=False)\n",
+    "    return abs(s[0]*s[1])>1e-12 # Basically 0 if separable, i.e. not entangled.\n",
+    "\n",
+    "psi = Statevector.from_label(\"00\")\n",
+    "local = QuantumCircuit(2) # A separable state.\n",
+    "for q in range(2): local.rx(0.7,q); local.ry(0.3,q); local.rz(0.2,q) # Example local unitaries. Change as desired.\n",
+    "psi_local = psi.evolve(local)\n",
+    "print(\"Entangled after local?\", entangled(psi_local)) #Whateve separable state, whatever local unitaries, should be False.\n",
+    "\n",
+    "ent = QuantumCircuit(2); ent.rxx(0.6,0,1) # An entangling operation.\n",
+    "psi_ent = psi_local.evolve(ent)\n",
+    "print(\"Entangled after RXX?\", entangled(psi_ent)) #Whatever entagnled state, whatever locc, should be True."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": ".venv",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
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+    "version": 3
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+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.8"
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+ "nbformat": 4,
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+}