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    "\"\"\"\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",
    "\"\"\""
   ]
  },
  {
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   "execution_count": 1,
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     "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."
   ]
  }
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