{
 "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": {
    "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
}
