Bell_CHSH.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3ea5fa78-b38c-460b-b924-5bd52a388184",
   "metadata": {},
   "source": [
    "# 1. Create Bell states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "04da4cba-6a73-4d17-86f4-0eb688838ef7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 267.052x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from numpy import pi\n",
    "\n",
    "qc = QuantumRegister(2, 'q')\n",
    "circuit = QuantumCircuit(qc)\n",
    "\n",
    "circuit.x(qc[0])\n",
    "circuit.x(qc[1])\n",
    "circuit.h(qc[0])\n",
    "circuit.cx(qc[0], qc[1])\n",
    "circuit.draw('mpl')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9361fb1f-fd0b-4841-8e57-a9f65b9e3ecf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statevector([ 0.        +0.j, -0.70710678+0.j,  0.70710678+0.j,\n",
      "              0.        +0.j],\n",
      "            dims=(2, 2))\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 2 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.quantum_info import Statevector\n",
    "from qiskit.visualization import plot_state_qsphere\n",
    "sv = Statevector.from_label('00')\n",
    "new_sv = sv.evolve(circuit)\n",
    "print(new_sv)\n",
    "plot_state_qsphere(new_sv.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "91c8fe4d-d94d-4267-ac6b-efa6307bf8f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5DLL9ZJgTqdw44O385jpGSZL6hM58Brmg1B4RLVRuInBjVxUlSVKtdcVnkA8Bv98F+5Ek6bjRFQH5h8AzXbAfSZKOG52ZpPMzXjhJJ6jcK3U4cGUX1yVJUk0dy40CDgP/DizOzCe7riRJkmrPGwVIklTQmREkABFxIXAWldOtj2fm4q4uSpKkWuvMZ5BjgO8CM6l8YTLA6IhoBi7JzKdfdGNJknqZzsxi/RpwCHhNZo7LzHHApGrb17qjOEmSaqUzp1jnAa/PzI1HGjJzQ0R8HHigyyuTJKmGOnsdZOlerC96f1ZJknqrzgTkA8CNETHuSENEvBq4AUeQkqQ+pjMB+XHgd4ANEfFURDwF/Fu17ePdUZwkSbXSmesgN0dEA/AG4Ixq8xOZ+aNuqUySpBp62RFkRPxeRGyKiKFZ8cPMvDEzbwR+Uu2b1wO1SpLUYzpyivWjwHWZubd9R2b+Avgb4KourkuSpJrqSECeA7zUadQHgeldU44kSceHjgTkqVRuTP5iEhjRNeVIknR86EhAbqEyinwx5wBbu6YcSZKODx0JyPuAv46IQe07IuJk4PPVdSRJ6jM6cpnHF4F3AOsi4m+BI9/9eCaVCTwBfKl7ypMkqTZeNiAzc2dEXAD8TypBGEe6gB8Af5qZO7qvREmSel6HbhSQmU8BF0fEMOA1VEJyfWbu6c7iJEmqlU59YXI1EH/STbVIknTc6Oy3eUiS1C8YkJIkFRiQkiQVGJCSJBUYkJIkFRiQkiQVGJCSJBUYkJIkFRiQkiQVGJCSJBUYkJIkFRiQkiQVGJCSJBUYkJIkFRiQkiQVGJCSJBUYkJIkFRiQkiQVGJCSJBUYkJIkFRiQkiQVGJCSJBUYkJIkFRiQkiQVGJCSJBUYkJIkFRiQkiQVGJCSJBUYkJIkFRiQkiQVGJCSJBUYkJIkFRiQkiQVGJCSJBUYkJIkFfRoQEbEnIi4NyK2RkRGxAfa9X+r2t52+Zd269RFxI0R8UxE7K/ub2xPvg5JUt/X0yPIwcBq4BPAgRdZ50fAaW2Wi9v13wC8HXgP8DpgKLAwIgZ0Q72SpH5qYE8+WWbeD9wPldHii6zWmpnbSx0R8Urgg8AfZeYPq23vA54C3gD8oKtrliT1Tz0akB00OyJ2As8CS4CrM3NntW8mcCKw6MjKmbk5Ip4ALqAQkBFxBXAFwOjRo1m8eDEAEydOZMiQIaxatQqAESNGMHXqVJYuXQrAwIEDmT17Ni0tLezduxeAxsZGKoNg9UXNzc0899xzAMyaNYstW7awdetWAKZMmcKAAQNYs2YNAKNGjWLChAksX74cgEGDBjFr1ixWrFjBgQOVkyNNTU1s3LiR7dsr7/fOOussDh06xNq1awEYM2YMY8eOZcWKFQAMHjyYxsZGli9fTmtrKwCzZ89m3bp17NxZOQSmTZtGa2sr69evB2DcuHGMHDmS5uZmAIYOHUpDQwPLli3j4MGDAMyZM4fHH3+cXbt2ATB9+nT27dvHhg0bABg/fjzDhw+npaUFgGHDhjF9+nSWLFlCZhIRzJ07l1WrVrFnzx4AGhoa2L17N5s2bQKO/njasWMHmzdvBmDSpEnU1dWxevVqAOrr65k8eTLLli0DoK6ujqampk7/P8EZnfxNUG+xbdu2Yz6eXkpkZjeW/xJPHPEc8NHM/Fabtj8E/h+wERgPfAEYAMzMzNaIuBS4FTgx2xQeEQ8C6zPzwy/1nI2NjXnkD8nRuvyGY9pcx7Gbr6p1BeoOHrN9V1ccsxGxMjMbS33H1QgyM+9o8/BnEbGSyunTNwN316YqSVJ/dFxf5pGZTwNbgEnVpu1URpSntFt1ZLVPkqQucVwHZEScAowBtlWbVgK/Bua1WWcscCbw4x4vUJLUZ/XoKdaIGAy8pvrwBODVETED2F1dPgfcRSUQxwNfBnYC3wXIzF9ExC3AtdWJPLuArwCPUbk8RJKkLtHTI8hG4P9Wl0HAX1V//jxwCDgbuAdYBywA1gJNmbmvzT6uohKY/wQ8AjwH/H5mHuqZlyBJ6g96+jrIxUC8xCpv6sA+WoGPVRdJkrrFcf0ZpCRJtWJASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJUYEBKklRgQEqSVGBASpJU0GsDMiI+EhEbI+KXEbEyIl5X65okSX1HrwzIiHg38FXgS8C5wI+B70fEq2tamCSpz+iVAQl8CvhWZt6cmU9k5seAbcCVNa5LktRH9LqAjIiTgJnAonZdi4ALer4iSVJfFJlZ6xo6JSJGA1uBuZm5tE37Z4H3ZuaUdutfAVxRfTgFWNtTtfYRpwDP1LoISR3i8dp5p2fmqaWOgT1dSU/LzJuAm2pdR28VEc2Z2VjrOiS9PI/XrtXrTrFSeXd0CBjZrn0ksL3ny5Ek9UW9LiAz81fASmBeu655VGazSpJ0zHrrKdavALdFxKPAI8CfAKOBv6tpVX2Tp6el3sPjtQv1ukk6R0TER4A/A04DVgOfbDtpR5KkY9FrA1KSpO7U6z6DlCSpJxiQkiQVGJCSJBUYkJLUB0REtP1Xx85JOpLUBx0JyvSP/FHrrddBqhtExKDMPFDrOiR1XEScALwNOBU4mcq9qpdk5s6aFtYHOIIUABExDFgF3AfcDvz4yDvPiIg2P58BPJ2Ze2tWrCQAImIIcAvwn4DDwBYggV8CS4DbMvPJtsewOs7PIHXEZVTuZzsTWAr8a0R8PiKmtAnHccD/pvKNAZJq7+NUvqXo4swcCbwXuAH4GfBG4NqIONVwPDqOIAVARNxM5SbwnwVGAe8B3gFMBH4C/D0wArg6MwfXqk5JvxERDwPfzcyvtGsfAPxHKqPLf8vM361Ffb2dI0gREXXAGmBzZu7MzMcy88+BRuBN1b7PAV8E/qZmhUp6XkQMpHKbzbdHxKnVtgERcUJmHqreevNPgLERMb2WtfZWjiAFPB+SwzJze/XdZ2bm4Tb9rwceBF6dmVtqU6WktiLitcA/AHcCX8nMHe36xwFPAFMyc2sNSuzVHEHqyCScVuDkiBhZffd5+EhfdbU5wCbDUTo+VGevNgPXAH8MPBkR/ysi5kXElIh4J/AF4AnD8eg4guznIqIeeB/wKWAncBDYBnwHuDsz91dD8nIqs1cX1qxYSUUR8SrgA8ClwAxgH5WZrD8BvpyZK2pVW29mQPZzEfEtYCrwf4DdwHDgXOAMKlPGr8vMRTUrUNJviYihwL62s1OrI8pXAIOBacB+g/HYGJD9WHVkuI/KFPGlbdrGAq+lMmo8HXhPZrbUrFBJLxAR3wAerS5Pla5LjohhmbnHayCPnp9B9m9nARuBXx1pyIrNmfkd4C1UAvSdNapPUjsR8R4qb17/B3APcF1E/EFEvCYiBlXXGQx8MyLONhyPniPIfqx6MC2kcnuq91O5Xupwu3U+BnwwM2f0fIWS2mtzzfK1wB8A84H/AKwF7gceoHLzgK9m5km1qrMvcATZj1Xvu3o1MAi4FXh/RIyrvvskIk4G5lK51kpSjVWvfdwIPJuZGzLz+sw8GziPyq3l5gPfBm4EbqtdpX2DI0gREdOA/w68FdgPLAf+HXgDlRmtH8rMn9WuQklHVO+bPLJ6j9WTgF+3m6zzbiq3hGzIzJ/WqMw+wYDU86qXfLwZ+M9UpoivBr6TmU/Wsi5JL606gzUy81BEXE7l9OrJta6rtzMgVVS9XdXhl19T0vEkIj4FDMjM62pdS29nQEpSHxIRJwKHfIN77AxISZIKnMUqSVKBASlJUoEBKUlSgQEpSVKBASlJUoEBKUlSwf8HfK3buXQBz6cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts = new_sv.sample_counts(shots=1000)\n",
    "\n",
    "from qiskit.visualization import plot_histogram\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b6e2eda-a722-4519-86b8-a4664c0d2ac9",
   "metadata": {},
   "source": [
    "# 2. Measurement"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65451f0c-66a5-45f5-b47b-bdecc6dfef7c",
   "metadata": {},
   "source": [
    "2.1 Measure on $Z$ axis and $(Z+X)/\\sqrt{2}$ axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "05e35f97-279f-4704-86f7-4d08546ac8bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#outcome1.1\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Given data\n",
    "data = {\n",
    "        \"00\": 0.0712890625,\n",
    "\t\t\"01\": 0.4306640625,\n",
    "        \"10\": 0.42041015625,\n",
    "\t\t\"11\": 0.07763671875,\n",
    "\n",
    "\n",
    "}\n",
    "\n",
    "# Extracting keys and values for plotting\n",
    "states = list(data.keys())\n",
    "probabilities = list(data.values())\n",
    "\n",
    "# Creating the bar chart\n",
    "plt.figure(figsize=(8, 5))\n",
    "plt.bar(states, probabilities, color='blue')\n",
    "plt.xlabel('Quantum States')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('$Z$ and $(Z+X)/\\sqrt{2}$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "61641e3c-fb04-4709-b762-ec2ba6ac4da1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.7021484375\n"
     ]
    }
   ],
   "source": [
    "#correlation coefficient \n",
    "#E1=E(Z,(Z+X)/\\sqrt{2})\n",
    "E1 = (data[\"00\"]+data[\"11\"])-(data[\"01\"]+data[\"10\"])\n",
    "print(E1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27e57d6a-9483-45a7-ac24-e147f07547c3",
   "metadata": {},
   "source": [
    "2.2 Measure on $X$ axis and $(Z+X)/\\sqrt{2}$ axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "ba0e5909-7486-4d06-b11c-22d4b7d17f2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#outcome1.2\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Given data\n",
    "data = {\n",
    "        \"00\": 0.4091796875,\n",
    "\t\t\"01\": 0.0791015625,\n",
    "        \"10\": 0.08447265625,\n",
    "\t\t\"11\": 0.42724609375,\n",
    "}\n",
    "\n",
    "\n",
    "# Extracting keys and values for plotting\n",
    "states = list(data.keys())\n",
    "probabilities = list(data.values())\n",
    "\n",
    "# Creating the bar chart\n",
    "plt.figure(figsize=(8, 5))\n",
    "plt.bar(states, probabilities, color='blue')\n",
    "plt.xlabel('Quantum States')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Probability Distribution of Quantum States')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "98cced83-5f75-4125-bb83-1218b62913e2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6728515625\n"
     ]
    }
   ],
   "source": [
    "E2 = (data[\"00\"]+data[\"11\"])-(data[\"01\"]+data[\"10\"])\n",
    "print(E2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42e2eb5c-d49b-44e8-aaa1-b4bcbdc9a3db",
   "metadata": {},
   "source": [
    "2.3 Measure on $Z$ axis and $(Z-X)/\\sqrt{2}$ axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "f8227610-0e81-4ac4-a4d3-a6347c26dda9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hSfYCbgOuA144qXokSVpsJnliG1W1Elg5bdgRA7cPm+TyJUlazOb9xDZJkrRmDHFJkhpliEuS1ChDXJKkRhnikiQ1yhCXJKlRhrgkSY0yxCVJapQhLklSowxxSZIaZYhLktQoQ1ySpEYZ4pIkNcoQlySpUWOFeJJ9kxj4kiQtIOMG83OA7yd5e5JHTLIgSZI0nrFCvKqeDzwG+AFwXJKvJDk4yaYTrU6SJM1o7C7yqvoZ8DHgJGBr4ADgnCSvmFBtkiRpFuMeE98/ySeBLwIbAbtX1T7ALsBrJleeJEmayYZjtnsG8O6qOmNwYFX9PMlL1n5ZkiRplHG7038yPcCTvA2gqj6/1quSJEkjjRviTxkybJ+1WYgkSZqbWbvTk7wM+DNgxyTfGhi1KXDmJAuTJEmzG3VM/ETgP4C3AocPDL+xqq6dWFWSJGmkUSFeVXVxkpdPH5HkgQa5JEnzZ5w98acBZwMFZGBcAQ+dUF2SJGmEWUO8qp7W/99h3ZQjSZLGNerEtt1mG19V56zdciRJ0rhGdae/c5ZxBey5FmuRJElzMKo7/XfXVSGSJGluRnWn71lVpyd5xrDxVfWJyZQlSZJGGdWd/mTgdGDfIeMKMMQlSZono7rT/6b//+J1U44kSRrXuD9FukWS9yY5J8nZSd6TZItJFydJkmY27g+gnARcBfwR8Mz+9kcmVZQkSRpt3N8T37qq3jRw/81JnjOJgiRJ0njG3RP/XJIDk2zQ/z0bOHWShUmSpNmN+orZjdx1zfQ/B07oR20A3AS8dpLFSZKkmY06O33TdVWIJEmam3GPiZNkc2AnYJOpYVV1xiSKkiRJo40V4kleChwGbAucCzwe+ApeO12SpHkz7olthwGPA37UX0/9McD1kypKkiSNNm6I31JVtwAkuVdVfRd4+OTKkiRJo4x7TPzSJJsBnwJOS3Id8KNJFSVJkkYbK8Sr6oD+5t8m+QLwAOD/T6wqSZI00lzOTt8N+B26742fWVW3TqwqSZI00rg/gHIEcDywBbAl8KEkr59kYZIkaXbj7ok/D9hl4OS2o+i+avbmCdUlSZJGGPfs9MsZuMgLcC/gsrVfjiRJGteoa6e/j+4Y+A3AeUlO6+8/Bfj65MuTJEkzGdWdvqr/fzbwyYHhX5xINZIkaWyjfgDl+KnbSTYGdu7vXlhVt42aeZK9gfcAS4Bjq+qoaeNfDbwUuB24CviTqvL755IkjWHcs9P3AL4PHA38A/C9JE8aMc2Svv0+wHLgoCTLpzX7BrCiqh4NfAx4+1yKlyRpfTbu2envBJ5aVRcCJNkZ+DDw2Fmm2R1YXVUX9dOcBOwPnD/VoKq+MND+q8Dzxy9dkqT127hnp280FeAAVfU9YKMR02wDXDJw/9J+2ExeAvzHmPVIkrTeG3dP/OwkxwIn9Pefx10nvd1jSZ4PrACePMP4g4GDAbbffvu1tVhJkpo27p74IXTd4K/s/84HXjZimsuA7Qbub8uQ75Yn2Qv4a2C/qvrlsBlV1TFVtaKqVixdunTMkiVJWtxG7on3J6h9s6oeAbxrDvM+C9gpyQ504X0g8Nxp834M8M/A3lX10znMW5Kk9d7IPfGqugO4MMmc+rGr6nbgUOBU4ALgo1V1XpIjk+zXN/t74H7Avyc5N8nJcytfkqT117jHxDenu2Lb14GbpwZW1X4zTwJVtRJYOW3YEQO39xq/VEmSNGjcEH/DRKuQJElzNura6ZvQndT2MODbwAf6bnJJkjTPRh0TP57uq1/fprvy2jsnXpEkSRrLqO705VX1mwBJPoC/XCZJ0oIxak/8Vz9yYje6JEkLy6g98V2S/Ky/HeDe/f0AVVX3n2h1kiRpRqN+inTJuipEkiTNzbiXXZUkSQuMIS5JUqMMcUmSGmWIS5LUKENckqRGGeKSJDXKEJckqVGGuCRJjTLEJUlqlCEuSVKjDHFJkhpliEuS1ChDXJKkRhnikiQ1yhCXJKlRhrgkSY0yxCVJapQhLklSowxxSZIaZYhLktQoQ1ySpEYZ4pIkNcoQlySpUYa4JEmNMsQlSWqUIS5JUqMMcUmSGmWIS5LUKENckqRGGeKSJDXKEJckqVGGuCRJjTLEJUlqlCEuSVKjDHFJkhpliEuS1ChDXJKkRhnikiQ1yhCXJKlRhrgkSY0yxCVJapQhLklSowxxSZIaZYhLktSoiYZ4kr2TXJhkdZLDh4x/UpJzktye5JmTrEWSpMVmYiGeZAlwNLAPsBw4KMnyac1+DLwIOHFSdUiStFhtOMF57w6srqqLAJKcBOwPnD/VoKou7sfdOcE6JElalCbZnb4NcMnA/Uv7YZIkaS1o4sS2JAcnWZVk1VVXXTXf5UiStCBMMsQvA7YbuL9tP2zOquqYqlpRVSuWLl26VoqTJKl1kwzxs4CdkuyQZGPgQODkCS5PkqT1ysRCvKpuBw4FTgUuAD5aVeclOTLJfgBJHpfkUuBZwD8nOW9S9UiStNhM8ux0qmolsHLasCMGbp9F180uSZLmqIkT2yRJ0q8zxCVJapQhLklSowxxSZIaZYhLktSoiZ6dLmn9lMx3BYtP1XxXoIXIPXFJkhpliEuS1ChDXJKkRhnikiQ1yhCXJKlRhrgkSY0yxCVJapQhLklSo7zYi5rhBUQmw4uISO1yT1ySpEYZ4pIkNcoQlySpUYa4JEmNMsQlSWqUIS5JUqMMcUmSGmWIS5LUKENckqRGGeKSJDXKEJckqVGGuCRJjTLEJUlqlCEuSVKjDHFJkhpliEuS1ChDXJKkRhnikiQ1yhCXJKlRhrgkSY0yxCVJapQhLklSowxxSZIaZYhLktQoQ1ySpEYZ4pIkNcoQlySpUYa4JEmNMsQlSWqUIS5JUqMMcUmSGmWIS5LUKENckqRGGeKSJDXKEJckqVGGuCRJjZpoiCfZO8mFSVYnOXzI+Hsl+Ug//mtJlk2yHkmSFpOJhXiSJcDRwD7AcuCgJMunNXsJcF1VPQx4N/C2SdUjSdJiM8k98d2B1VV1UVXdCpwE7D+tzf7A8f3tjwG/lyQTrEmSpEVjkiG+DXDJwP1L+2FD21TV7cANwBYTrEmSpEVjw/kuYBxJDgYO7u/elOTC+axnHm0JXD3fRYzD/hTXVUOaWFeupzbWE0xkXT1kphGTDPHLgO0G7m/bDxvW5tIkGwIPAK6ZPqOqOgY4ZkJ1NiPJqqpaMd91aDTXVTtcV21wPQ03ye70s4CdkuyQZGPgQODkaW1OBl7Y334mcHpV1QRrkiRp0ZjYnnhV3Z7kUOBUYAnwwao6L8mRwKqqOhn4APCvSVYD19IFvSRJGsNEj4lX1Upg5bRhRwzcvgV41iRrWGTW+0MKDXFdtcN11QbX0xCx91qSpDZ52VVJkhpliC9Qwy5Z258k+LV+2Ef6EwY1z2ZYV4f29yvJlvNdoyDJB5P8NMl3BoY9MMlpSb7f/998PmtUZ4Z19awk5yW5M4lnqfcM8QVolkvWvg14d3+Z2uvoLlureTTLujoT2Av40TyWp7s7Dth72rDDgc9X1U7A5/v7mn/H8evr6jvAM4Az1nk1C5ghvjDNdMnaPekuTwvd5WqfPj/lacDQdVVV36iqi+e3NA2qqjPovgUzaPDSz76mFohh66qqLqiq9fVCXzMyxBemmS5Ze31/edrBYZpf41xeWAvXVlV1RX/7J8BW81mMNFeGuCQB/YWm/LqOmmKIL0wzXbJ2s/7ytIPDNL/GubywFq4rk2wN0P//6TzXI82JIb4wzXTJ2i/QXZ4WusvVfnqe6tNdxrm8sBauwUs/+5pScwzxBag/7j11ydoLgI9W1XnAXwKv7i9TuwXdZWs1j2ZaV0lemeRSuj3zbyU5dj7rFCT5MPAV4OFJLk3yEuAo4ClJvk/3bYKj5rNGdYatqyQH9K+pJwCnJDl1fqtcGLximyRJjXJPXJKkRhnikiQ1yhCXJKlRhrgkSY0yxCVJapQhLi0gSbZN8un+V7UuSvL+JPeawHL2SPLba3u+/by3SvLZJN9Mcn6Slf3wZUmeO8b0Y7WTZIhLC0aSAJ8APtX/qtZOwL2Bt09gcXsAEwlx4EjgtKrapaqWc9cvgy0DxgnncdtJ6z1DXFo49gRuqaoPAVTVHcCrgD9Ocr8kL0ry/qnG/d7uHv3tf0yyqv+95TcOtLk4yRuTnJPk20kekWQZcAjwqiTnJnlikuOSPHNgupv6/3sk+VLfO3BRkqOSPC/J1/v57TjkcWxN90Mw9I/jW/3No4An9st8Vb/H/eW+tnMGegamt1uS5O+TnJXkW0n+tK9t6yRn9O2+k+SJ9+TJl1q04egmktaR3wDOHhxQVT9LcjHwsBHT/nVVXdv/vvnnkzx6IDyvrqrdkvwZ8NqqemmSfwJuqqp3APRXL5vJLsAj6X4a8iLg2KraPclhwCuAP5/W/mjgI0kOBf4T+FBVXU63R/7aqnpav8z7AE+pqluS7AR8GFgxpN3BwA1V9bj+0MKZST5H99vSp1bVW/rHfZ8Rz5G06Bji0uLw7D7sNqTbE14OTIX4J/r/Z9MF31ydNfVznUl+AHyuH/5t4HenN66qU5M8FNgb2Af4RpJHDZnvRsD7k+wK3AHsPMPynwo8eqCn4AF0hxrOAj6YZCO6QxDnrsFjk5pmd7q0cJwPPHZwQJL7Aw8CLgRu5+6v2U36NjsArwV+r6oeDZwyNa73y/7/Hcz8wf1X806yAbDxkOkB7hy4f+dM86uqa6vqxKp6AV3YPmlIs1cBV9Lt6a+YtsxBAV5RVbv2fztU1eeq6ox+vpcBxyX54xmmlxYtQ1xaOD4P3GcqjPou4ncC76+qXwAXA7sm2SDJdsDu/XT3B24GbkiyFd3e7yg3ApsO3L+Yuz5A7Ee3l7xGkuzZd5WTZFNgR+DHQ5b5AOCKqroTeAGwZIbaTgVe1u9xk2TnJPdN8hDgyqr6F+BYYLc1rVlqlSEuLRDV/RrRAcAz+1/Vuga4s6re0jc5E/gh3R77e4Fz+um+CXwD+C5wYt9ulM8AB0yd2Ab8C/DkJN+k+5Wom+/BQ3kssCrJt+h+ierYqjqLrnv/jv6rZ68C/gF4Yb/MRwwsc3q7Y/vHfE6S7wD/TNcDsAfwzSTfAJ4DvOce1Cw1yV8xkxao/mztDwMHVNU5812PpIXHEJckqVF2p0uS1ChDXJKkRhnikiQ1yhCXJKlRhrgkSY0yxCVJapQhLklSo/4HY4oSMVV5PuYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#outcome1.3\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Given data\n",
    "data = {\n",
    "        \"00\": 0.4306640625,\n",
    "\t\t\"01\": 0.0673828125,\n",
    "        \"10\": 0.08203125,\n",
    "\t\t\"11\": 0.419921875,\n",
    "}\n",
    "\n",
    "\n",
    "# Extracting keys and values for plotting\n",
    "states = list(data.keys())\n",
    "probabilities = list(data.values())\n",
    "\n",
    "# Creating the bar chart\n",
    "plt.figure(figsize=(8, 5))\n",
    "plt.bar(states, probabilities, color='blue')\n",
    "plt.xlabel('Quantum States')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Probability Distribution of Quantum States')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "2cc2c40f-c194-4754-9bb2-5c0ae63f6541",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.701171875\n"
     ]
    }
   ],
   "source": [
    "E3 = (data[\"00\"]+data[\"11\"])-(data[\"01\"]+data[\"10\"])\n",
    "print(E3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c23305af-c74b-4011-93c3-75d3eb6f7ec7",
   "metadata": {},
   "source": [
    "2.4 Measure on $X$ axis and $(Z-X)/\\sqrt{2}$ axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "6dbd81d7-a8d7-431a-8ffe-c3dbd850f9fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#outcome1.4\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Given data\n",
    "data = {\n",
    "        \"00\": 0.435546875,\n",
    "\t\t\"01\": 0.060546875,\n",
    "        \"10\": 0.068359375,\n",
    "\t\t\"11\": 0.435546875,\n",
    "}\n",
    "\n",
    "\n",
    "# Extracting keys and values for plotting\n",
    "states = list(data.keys())\n",
    "probabilities = list(data.values())\n",
    "\n",
    "# Creating the bar chart\n",
    "plt.figure(figsize=(8, 5))\n",
    "plt.bar(states, probabilities, color='blue')\n",
    "plt.xlabel('Quantum States')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Probability Distribution of Quantum States')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "e69f0701-a329-46eb-81d4-1366cf565fa5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7421875\n"
     ]
    }
   ],
   "source": [
    "E4 = (data[\"00\"]+data[\"11\"])-(data[\"01\"]+data[\"10\"])\n",
    "print(E4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bab6035b-888c-4665-bdfc-846efcf0aea6",
   "metadata": {},
   "source": [
    "# 3. Check the Bell-CHSH inequality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "3e1c6db6-21ff-47eb-92d1-1dee4ad150a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.818359375"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-E1+E2+E3+E4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "44672cd0-59bd-4272-9c12-f219200c9c77",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "0f463ccd-b849-4663-a270-7fdc3606db38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.8284271247461903"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*math.sqrt(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6cb07f9f-e8cb-4423-9fdb-948fcd6aa1de",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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