02. Entangled States and Superdense Coding.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "229179a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "from qiskit.quantum_info import Statevector\n",
    "\n",
    "from qiskit import Aer\n",
    "backend = Aer.get_backend('aer_simulator')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77539fd5",
   "metadata": {},
   "source": [
    "## Intro\n",
    "let's start by drawing some kets and changing ket state using some gates\n",
    "for some reasons, i can't find ~/.qiskit in my laptop, so I'll add parameter inside each draw method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "69db8365",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ |00\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "\n",
    "# This calculates what the state vector of our qubits would be\n",
    "# after passing through the circuit 'qc'\n",
    "ket = Statevector(qc)\n",
    "\n",
    "# The code below writes down the state vector.\n",
    "# Since it's the last line in the cell, the cell will display it as output\n",
    "ket.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "17177357",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ |00\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.cx(0,1)\n",
    "\n",
    "ket = Statevector(qc)\n",
    "ket.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0957f9df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ |00\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.cx(1,0)\n",
    "\n",
    "ket = Statevector(qc)\n",
    "ket.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "aaf1f1b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ |10\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.x(1,0)\n",
    "\n",
    "ket = Statevector(qc)\n",
    "ket.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3d182b8d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ |11\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.cx(1,0)\n",
    "\n",
    "ket = Statevector(qc)\n",
    "ket.draw('latex')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "999f4dd3",
   "metadata": {},
   "source": [
    "## Create entanglement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8c04469d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\sqrt{2}}{2} |00\\rangle+\\frac{\\sqrt{2}}{2} |10\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's create a fresh quantum circuit\n",
    "qc = QuantumCircuit(2)\n",
    "\n",
    "qc.h(1)\n",
    "\n",
    "ket = Statevector(qc)\n",
    "ket.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "42660c51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\sqrt{2}}{2} |00\\rangle+\\frac{\\sqrt{2}}{2} |11\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.cx(1,0)\n",
    "\n",
    "ket = Statevector(qc)\n",
    "ket.draw('latex')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0d2245f",
   "metadata": {},
   "source": [
    "and that, is an entangled state"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63317407",
   "metadata": {},
   "source": [
    "## Superdense coding"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b02cf8c",
   "metadata": {},
   "source": [
    "Intro to sending and receiving messages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2ec76c0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 146.652x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The message - play with it\n",
    "MESSAGE = '01'\n",
    "\n",
    "# Alice encodes the message\n",
    "qc_alice = QuantumCircuit(2, 2)\n",
    "if MESSAGE[-1]=='1':\n",
    "    qc_alice.x(0)\n",
    "if MESSAGE[-2]=='1':\n",
    "    qc_alice.x(1)\n",
    "    \n",
    "qc_alice.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "23d01cee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 206.852x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Bob measures\n",
    "qc_bob = QuantumCircuit(2,2)\n",
    "qc_bob.measure([1,0],[1,0])\n",
    "\n",
    "qc_bob.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "bff461a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMYAAABjCAIAAABPKOhXAAAN3UlEQVR4nO2df0wT5x/HH7ryQ4qgKL9/Y3BhgCOLyPjlGKD7oRimAhoHG5vJotPECCwGI+hU5mAj2XRxyZYZxlhUprK5ucmgwAAR0GaTicgaSu1KISBUes62lHu+f5zfroP2+ut616vP66/e9e7zefPw7t1zzz33OScIIUDYEmdnZ41GQ1s6Lpc7OztLW7qFOCFL2RonJ1obmeZ0C+EymJsqbHEYYPy3zl4cwVIajYby36WTkxO1AZ8cOEwLQFjIt99+q1KpmFahB2QpVnL9+vUDBw4wrUI/yFKspKSk5NixY66urkwL0YMj9KUW8ujRI6lU6uLiwuFwAABqtdrT03P58uUAALFYrNFonJ2dIYRqtTokJMTNzY1pvebR0NCAYdjrr7/OtBADwP+D4/i9e/dUKhWxqP1g/+j+FQQSieTQoUPp6enE35icnNzc3Ex8VV1d7eXlBQBYs2ZNSUnJ2NiYiTEplGcNKpUqKirq119/pSedBTxO39nZuXHjxjNnzlRUVLS0tOzatUv7PzAdpVKZlpa2Z88eqkUawVAjzs3NvfLKKwCAM2fO6K5/5513Dhw4YFlMCuVZRk1NTXZ2Nm3pLABACC9cuBAVFTU+Pk6sysvLc3Z2fvjwobmxxsfHXVxcYmNjKdZoDJJGlEgkXl5e3t7eMpmMWDMyMpKXl2dNTArlmcvU1JSvr++ff/5JTzrLADKZzNPTs66uTrvqzTffTElJIT739fUdPXq0pqbm6tWrpoSTSqUzMzM2UWoY8kb88ssvAQCbNm2CEOI4vmXLFqlUamVMCuWZxf79+3ft2kVbOssAO3fu9PDwUCqV2lUrVqwoKyuDEN68eXPr1q2zs7MQwvLy8srKSsZkkmK0EdevXw8AqKurO3XqVH19PSUxTYeqUMPDw8uWLdMebm2dzmJAYGDghg0btMsSiQQA0NTUBCFMSEjQ9qiUSqWXl9eDBw+YkUmK0UYUi8WLFy9eunRpYWEhVTFNh6pQubm5x48fpy2dxXBGR0dTUlK0F4B8Pp/L5SYnJ8vl8hs3bqxYsYJY7+rq6uXl1dTUZJPLThsTGhpaXV09PT2tUCiY1mISGIaNj49LJJLp6Wm1Wg0A6Onp6e7u3rdvH9PSjMMFAERFRWmXm5ubExISeDxeb28vhNDd3V37lbu7+9jYGHm46elpd3d3o0NwERERIyMjlqs2H4VCERkZeenSpXPnzuXn55uyC523+UQiEZ/Pb29vv3379tDQEADAw8PDxcVFoVA8evTI399fLpenp6dfu3Zt7dq1Li4u5NGsUc7lcq25Bx8eHs6JjY2Vy+XEcmtr69mzZ1944QUAAHH/SFccjuMPHjwgCXf//v2QkJDU1FSjiUUiEYVHWqPpBgYGbt++zefzPTw89uzZMzExYXQXQOmJzxAYhn322WfPP/98UlJSW1tbWlra559/LpVKFQqFTCYTi8VTU1MKhaK4uHjp0qXPPPNMRUVFYGDgzp07b968aSPlRNfZYkQiEejt7U1LS7t48WJVVdWJEycAAL/88guE8PfffwcAjI6Oarf28/P75JNPSML9888/cXFxBQUF1miyAPJGnJ2d3bhx4+TkJITw9OnTAAB7GETAMKyiosLHxycvL+/q1avEZAq9zBvblEgkVVVVYWFh6enpXV1dNlVuGQBCqFQq+/v7VSrV119/zeVyFQoFhFClUrm5uf3xxx/aTV1dXTs6OhhTahjyRjxy5Mj3339PfMZx/MUXXwQAXLhwwZqYVsr77rvvQkNDCwsLhUKh0d0//vjjhWObs7OztbW1ISEhO3bsmJiYIE9HM/9J/9ZbbyUmJmoX33jjDe248/Dw8NNPP22fd2lIGlEgELz99tu6a4aHh3k8np+fH3HcsiCmNfIwDCsqKoqOju7s7DRlX/KxTQzDSktLg4KCdO/P2JGl5ubmwsLCSkpKtGump6dfeumlS5cudXZ2bt68meiw2yGGGnF4eHjlypXEgIguR44cAQBs3bqV5HRjC0tJpdJVq1YVFRVhGGbivqaMbba0tAQFBZ08eXJeOqZ4nL68vDw9Pd3Z2TkmJmb//v3arzUaTV9f32+//UacDe2ThY3Y0NCQmZnp7e3N4/F8fHx0T3NVVVXBwcGenp6enp4JCQnbtm3Te+uJckuJRKKIiIgTJ06YvuPw8PDy5cuNjm1CCEdGRqKjo6urq6EdWOrx1HeNRsPlPp7oovuZFdhiAj+FMYlQg4ODAwMDmzdvNn3HvLy8+Pj4srIyUzaWy+VisfjZZ59l/HEGR3hChhWWMncvoVCYkZFx9+7dRYsW0ZCOQpClbB7TslAQwunpaW9vb3rSUQiylM1jPmnP8aG55wiKQZZCUAybruwMweVyKb/Fy65rXrvCERrOzp80t4XjydPRlksvjtA9dzx0u9iMd7fNBfWlEBSDLIWgGGQpBMWwsnv+pNWVYxestJQtCkqRgGpNmQU68SEoBlnqX/r7+5mW4AggSz2mu7s7OzubaRWOALLUY0pLS48ePcq0CkcAWQoAABoaGh4+fLhjxw6mhTgC/1oKQiiRSIjHpQEA2g8Oj1qtLisrq66uJkrmIazkcSN2dXVt2rSppaWlsrKSz+fv3r27o6PD3FgqlWrt2rV79+6lWqRtOXXqVHR0dFZWFtNCHAXIwpJlwNGLgOlmpD+7lXDGxsaKiorKy8t9fX0Jk7m7u69Zs0ZbYGNsbKyystIUd/r6+opEomvXrtnC+jbi2LFjW7ZsiYmJYVqIA0FSsqy7u/vgwYOFhYXh4eHMmV4PgLoiYKY8KEdVOtMBbD5KkZUsI2hsbHRUS9ltETBWW8pgyTL6j5c0w6IiYOzCYMkyy8LZT8kyjUYjEAg6Ojru3LkzNDQ0MTGBYRiO425ubj4+PpGRkV1dXdu3b5+bmzMlGv13jp2cnLTVw2ieZ2xlyTLuwpJlxcXFloW7f/9+WFhYdHR0X18f+ZYikciyFAQkTQwhbGtrq6ura2xsDA4OTk9PT0xMLCgo8Pf35/F4HA5HqVROTEzU19crlcqenp7g4OC0tLT8/Pzc3FyS1zRAeqfqsnqiMPerr74qLi5etmyZUCjEcXx2dlb7UgNzcXd3j4yMjI6OplShqeA4fu7cuQ8//BBCWFRUdPz48YCAAL1bBgcHFxQU1NfXZ2VlYRh2+fLlb7755r333tu9e/e+ffsWL15Ms3JHAxooWaaFFd3zGzduJCYmJiUl/fzzzziOk++u9wUHAwMDBQUFQUFBtbW1RtPZGsDm7jlZyTKCixcvhoaG0ijJOLqtrNFo3n///YCAgNraWqNmgsbGNnt6ep577rmcnBzdgmbIUmZBVrLszp075eXlmZmZS5YsKS4urqmpYUKhHrStLJfLs7KyMjMzdWuKkmO0CJhKpSotLQ0NDe3v75+XjjYcwVKGSpbZJ0Qry2Sy+Pj4vXv3zs3NmbijiS84gBCePXvWz8+PKH+ILGUWrCxZRlwENTY2CoXCkpIS03fMz89ftWrVwYMHTdm4q6tLpVJlZGTQf83F6is+lsklsKyVBQJBTk7O4OCg7vsBbJfOGpCl6MayVp6cnJTJZHFxcfSkswZkKbpx+CJgrLYUmseIoBhkKQTFIEshKAZZCkExdj3+ZIgnra4cu2DZ1YTFsOsail1q54FOfAiKQZZCUAyyFIJikKUQFIMshaAYZCkExSBLISjGYS2F4/jhw4dJRnQghIcPH8ZxnE5VhmCXWnIc1lIcDmdmZuaDDz4wtEFlZaVCobCTmlLsUmsEWqYjM4NarU5NTW1ra4MLZnO3trampqaq1Wrm1M2HXWpJcGRLQQjFYnFsbOz4+Pi8f1JsbOy9e/cYFKYXdqk1hKmW+uuvv1pbW7VlzVjEjz/+uG7dOu3TrTiOL1q06KeffmJWlSHYpVYvxs/N7e3tCQkJfD4fAHD69OlDhw4Z6iTaZ2HFDRs2BAUFnTx5kli8fPnytm3bXn31VWZVGYJdavVD7rj29nYulysQCIjFxsZGHo/X3Nysd2PaCiuay927d1NSUojPycnJQ0NDzOohh11qF2LEUjExMS+//LJ2sbm5OT4+fnBw0ND2Uql0ZmbGaNbw8HBGfj9PPfUUI3ktgxG1Vk4OCw8PJ7MUURGvuLjYqEXsn1u3bq1bty4rK+vWrVtMazEOu9TOg8ySQqEQAODv72+Nbe2EuLg4pVLJ4XAseI6Pftildh5kliKq4xHHKgfgo48+YtFr0Nil9j+QH8Ti4uLS0tJ016hUqh9++MHQ9lNTU7rFiQ3BVF+KXbPIGVFr274UhPD69etcLvfKlSvaNZ9++mlfX5/ejScnJ3k83urVq41aCuHAGLFkYmJiZ2fnu+++29XVRVzrxcTErF69Wu/GzBZWRNgJpj59MT4+LpfLV65cydYTPIIuWPZAD8L+YcNkCQSrQJZCUAyyFIJikKUQFMOmoT+LEYlEHR0dX3zxxfnz5w29ssF+GBsbO3/+vL+//8TERHZ2dmhoKNOKzITpgTE6GB0dlclksbGxIyMjTGsxzvr166VSKYRwcnIyIyODaTlm80Sc+AICAthy83tqaqqvry8wMBAAQLzY5++//2ZalHk8EZZiEVKp1NPTU7u4ZMkSZCmEVXh4eGAYpl3EMMzDw4NBPRaALGVfRERE8Hg8tVoNACDessS6e6ZPxA0ZgUDQ0tJSU1Ozffv2pKSk3NxcphWR0dTU1Nvb+9prr125ciUqKionJ4dpRebxPyFEy1BYOpqfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=198x99 at 0x7FC612D15F10>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_alice.compose(qc_bob).draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "84857304",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'01': 1024}"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend.run(qc_alice.compose(qc_bob)).result().get_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f79f3edc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'01': 1024}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_compose = qc_alice.compose(qc_bob)\n",
    "backend.run(qc_compose).result().get_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c6ea492",
   "metadata": {},
   "source": [
    "Now add some entanglement - one way is to add cx gate after h gate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a881cc8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\sqrt{2}}{2} |01\\rangle+\\frac{\\sqrt{2}}{2} |10\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MESSAGE = '01'\n",
    "\n",
    "qc_alice = QuantumCircuit(2,2)\n",
    "\n",
    "# Alice encodes the message\n",
    "if MESSAGE[-1]=='1':\n",
    "    qc_alice.x(0)\n",
    "if MESSAGE[-2]=='1':\n",
    "    qc_alice.x(1)\n",
    "\n",
    "# then she creates entangled states\n",
    "qc_alice.h(1)\n",
    "qc_alice.cx(1,0)\n",
    "\n",
    "ket = Statevector(qc_alice)\n",
    "ket.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c5009865",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=168x86 at 0x7FC612C26250>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_alice.draw('latex')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cf5eb65",
   "metadata": {},
   "source": [
    "Using above message encoding and circuit, Alice converts 2-qubit messages into entangled state:\n",
    "![alt text](images/image1.png \"message to entangled state\")\n",
    "which then Bob untangle it by doing the 'inverse'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7bb3c577",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'01': 1024}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_bob = QuantumCircuit(2,2)\n",
    "# Bob untangles\n",
    "qc_bob.cx(1,0)\n",
    "qc_bob.h(1)\n",
    "# Then measures\n",
    "qc_bob.measure([0,1],[0,1])\n",
    "\n",
    "backend.run(qc_alice.compose(qc_bob)).result().get_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b422e5a",
   "metadata": {},
   "source": [
    "But above method doesn't take the advantage of entanglement.\n",
    "Here's how"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "91f1189d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\sqrt{2}}{2} |01\\rangle+\\frac{\\sqrt{2}}{2} |10\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MESSAGE = '10'\n",
    "\n",
    "qc_alice = QuantumCircuit(2,2)\n",
    "qc_alice.h(1)\n",
    "qc_alice.cx(1,0)\n",
    "\n",
    "if MESSAGE[-2]=='1':\n",
    "    qc_alice.x(1)\n",
    "if MESSAGE[-1]=='1':\n",
    "    qc_alice.z(1)\n",
    "\n",
    "ket = Statevector(qc_alice)\n",
    "ket.draw('latex')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f46677e",
   "metadata": {},
   "source": [
    "*check the ket for each message, especially for '10' and '01', compare with previous message encoding and circuit result*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "361c3184",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'10': 1024}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_bob = QuantumCircuit(2,2)\n",
    "# Bob untangles\n",
    "qc_bob.cx(0,1)\n",
    "qc_bob.h(0)\n",
    "# Then measures\n",
    "qc_bob.measure([0,1],[0,1])\n",
    "\n",
    "backend.run(qc_alice.compose(qc_bob)).result().get_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1291c335",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=371x99 at 0x7FC612C6FCD0>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_alice.compose(qc_bob).draw('latex')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da3b0f56",
   "metadata": {},
   "source": [
    "The important thing to note here is that the x and z gates can be applied to just a single qubit (qubit 1 in this case). This means that Alice could send qubit 0 to Bob as soon as she has created the entangled pair. In fact, she could send it before she even knows what message she wants to send!<br>\n",
    "<br>\n",
    "(from Qiskit textbook)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "140c8962",
   "metadata": {},
   "source": [
    "## Add Charlie\n",
    "Another scenario: There's a third party, Charlie, whose job is just to create entangled states, send one qubit to Alice, and send another to Bob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "938454b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\sqrt{2}}{2} |00\\rangle+\\frac{\\sqrt{2}}{2} |11\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_charlie = QuantumCircuit(2,2)\n",
    "\n",
    "qc_charlie.h(1)\n",
    "qc_charlie.cx(1,0)\n",
    "\n",
    "ket = Statevector(qc_charlie)\n",
    "ket.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "5aca3d38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=168x81 at 0x7FC612C6F040>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_charlie.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "654903fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=176x79 at 0x7FC612B4A1F0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MESSAGE = '11'\n",
    "\n",
    "qc_alice = QuantumCircuit(2,2)\n",
    "\n",
    "if MESSAGE[-2]=='1':\n",
    "    qc_alice.x(1)\n",
    "if MESSAGE[-1]=='1':\n",
    "    qc_alice.z(1)\n",
    "    \n",
    "qc_alice.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "74987600",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=236x99 at 0x7FC6704E44F0>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_bob.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "4a673b2b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'11': 1024}"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "complete_qc = qc_charlie.compose(qc_alice.compose(qc_bob))\n",
    "backend.run(complete_qc).result().get_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "52a6f1c2",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 507.852x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "complete_qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "135dfbda",
   "metadata": {},
   "source": [
    "👍"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49e6e1a7",
   "metadata": {},
   "source": [
    "commentary:<br>\n",
    "it'd be better if we can do qc1 + qc2 + qc3 instead of qc1.compose(qc2.compose(qc3))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.10 64-bit",
   "language": "python",
   "name": "python3810jvsc74a57bd0916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}