03. Hardy Paradox.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "229179a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "\n",
    "from qiskit import Aer\n",
    "backend = Aer.get_backend('aer_simulator')\n",
    "\n",
    "from math import pi\n",
    "from qiskit.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77539fd5",
   "metadata": {},
   "source": [
    "## Measurements"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01f5cd84",
   "metadata": {},
   "source": [
    "first, x-measurement: adding H gate before measure gate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "69db8365",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=180x66 at 0x7F2BF823A5E0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "meas_x = QuantumCircuit(1,1)\n",
    "meas_x.h(0)\n",
    "meas_x.measure(0,0)\n",
    "\n",
    "meas_x.draw('latex')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5974ac23",
   "metadata": {},
   "source": [
    "z-measurement: just a measure gate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ccdd59bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=152x82 at 0x7F2BF823A250>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "meas_z = QuantumCircuit(1,1)\n",
    "meas_z.measure(0,0)\n",
    "\n",
    "meas_z.draw('latex')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b424218",
   "metadata": {},
   "source": [
    "there's also something called y-measurement, but we'll save it for later.<br>\n",
    "now do some measurement on different qubits/states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dc9f7b0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=73x56 at 0x7F2BFE5F9EE0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using |0>\n",
    "qc = QuantumCircuit(1,1)\n",
    "\n",
    "qc.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0e3cf6eb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results from z measurement: {'0': 1024}\n",
      "Results from x measurement: {'0': 503, '1': 521}\n"
     ]
    }
   ],
   "source": [
    "print('Results from z measurement:',\n",
    "      backend.run(qc.compose(meas_z)).result().get_counts())\n",
    "print('Results from x measurement:',\n",
    "      backend.run(qc.compose(meas_x)).result().get_counts())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fa6646c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=122x55 at 0x7F2C39C139D0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using |1>\n",
    "qc = QuantumCircuit(1,1)\n",
    "qc.x(0)\n",
    "\n",
    "qc.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5590d515",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results from z measurement: {'1': 1024}\n",
      "Results from x measurement: {'1': 498, '0': 526}\n"
     ]
    }
   ],
   "source": [
    "for basis,circ in [('z', meas_z), ('x', meas_x)]:\n",
    "    print('Results from ' + basis + ' measurement:',\n",
    "      backend.run(qc.compose(circ)).result().get_counts())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7c18d5b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHoAAAA3CAIAAABM/ckBAAAFZElEQVR4nO2bT0gbTxTHX9ZJ0ia2l4JpQ4vbQA6aFYqatljUHFoQlZ5aKUKF9lJo8ZRLLyJ48GDwoBA8BHrxUG0piC0G2iQkRqHakoO1JGlTDNT80YaKRiFWs/M7rMTU3yZVE2djsp9D2J0wbx7f93Z2mHkrwRhDQSKVSnd3d/NrEyG0s7OTX5tHQlKwcksk+fftJGweCUrAsUsQUW6iiHITRZSbKCh1hTFeXl5WqVQymQwA/vz5w10UFPF4fHV1VSaTURSFMU4mkxhjmqa3trYikYhcLpdIJACQTCaTyaRGoxHa34PsZffs7Ozdu3ftdnt/f7/D4Xj69Knb7ebtsL293dTU1N3dTdDJfaLR6MuXLx8/fnz58uXq6uqRkRGHwwEAsVhsbGzsyZMnV65c0Wq1ZrP5/fv3gnj4DzDGb9680Wq1KysrGGOMcUdHh1Qq3drawnysrKzIZDKGYXj/zSOcb7x8/vwZANrb2w+0+3w+ADAYDMewSQYUjUYfPXpkNpsrKiq4ACgUiuvXrysUCt7wVFRULC0tnTt3jlA68HHmzJnU72HaCweqp6eHZdn79++nmtxud3Nzc5Y+arVaWLlPL9TU1FRzc7NcLuful5eXf/z4YTAYBPWqaKHC4fCtW7dS9w6HAyHU0NAgoE9FDAIArVaburfZbHq9XqlUZumztramUChSD0QWrl69GgwGc3aSn/n5+YcPH6a3bG5u/rMXt1I8HgihXHbNaJoGhmEsFgv33nQ4HFKp9Pnz51nerbFYTKlU1tfXn/RLHDKvIhYXFwHg3r17B9q50La0tBzDJhnQixcvjEbjhQsXAoEAy7I7OzvZJ26FQqHRaKqqqo4d5FIG6fX6Dx8+fP/+va2tbXx8HCGUPpX/n7Nnzy4sLBDzr8hAACCXyxmGAQCn01lXV1deXi60V0XL/hYVy7J2u72xsVFAb4qevS2q3t7e6enpcDhstVpZlh0cHBTWreysr68DwMbGBm8791uY7B0m7e7uIrQnffq1gPAedHk8nqGhIa/X++3bN6lUevv2ba1W29fX9/XrV5PJ5Pf7vV4vRVF37typrKwcGBg4jE2SiGeVRBGPF4giyk0UUW6iiHITRZSbKMIv+DKBEMpl9y6TzfwaPCqFuxAsSsTJhCii3EQR5SaKKDdRRLmJUhByW63WeDwutBckEH4hiDFmGGZubq4UTpGEz263211bW1sKWkMhyD06OnqgXKSIEXgySSQStbW1X758KSsrE9ANYvyV3YFAwOl0rq6uEhv+7du3ra2tJaI1pOR2uVx6vZ4rTR8ZGeHKYnk75LecfnR0tKurKy+mTgcYY5fLhRDyeDxcYdXExIRSqbTZbLxlV3ksp//161ddXV3udk4RgDHW6XTpdXU2m+3atWs+ny9Tn1AotLGxcRjrNE0TyBhi26o5DkTTNPz8+RMAjEZj7qE7Kjdv3gyFQuTHFRAqEAgAwMWLF/OTAIfG7/efP39erVYTHldYKK64m8txkpTUcnsfjHFNTU1jY2N6zm9vb09OTmZ6In7//p1IJA7z7Ihzdzo0TQPG+OPHjwihqamplEzDw8OfPn3iVTAv5fQul6urqysXC6cUBAA3btyYmZl59uzZ7OwstybR6XT19fW8IcpLOX2mmWRpacntdlssllevXl26dCmXIQqUdO2j0ajP52NZ9kQjnEgkqqurue+rDxAOhyORCMMwwWDwRH0Qir8mI5VKpVKpTjrAk5OT7e3tFMWzO1acGZ2GADuCJbomAQDycsdisWg0yn2bUoKQlntsbOzBgweEBy0cSMv97t27zs7OTP96PB6TyRSLxYaGhl6/fk3SMTL8B+qxSFwDnIp8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=122x55 at 0x7F2C514C8850>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using |+>\n",
    "qc = QuantumCircuit(1,1)\n",
    "qc.h(0)\n",
    "\n",
    "qc.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c41cce4e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results from z measurement: {'0': 477, '1': 547}\n",
      "Results from x measurement: {'0': 1024}\n"
     ]
    }
   ],
   "source": [
    "for basis,circ in [('z', meas_z), ('x', meas_x)]:\n",
    "    print('Results from ' + basis + ' measurement:',\n",
    "      backend.run(qc.compose(circ)).result().get_counts())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f02bab51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=171x55 at 0x7F2C39C13AF0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using |->\n",
    "qc = QuantumCircuit(1,1)\n",
    "qc.x(0)\n",
    "qc.h(0)\n",
    "\n",
    "qc.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "68a93b68",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results from z measurement: {'0': 507, '1': 517}\n",
      "Results from x measurement: {'1': 1024}\n"
     ]
    }
   ],
   "source": [
    "for basis,circ in [('z', meas_z), ('x', meas_x)]:\n",
    "    print('Results from ' + basis + ' measurement:',\n",
    "      backend.run(qc.compose(circ)).result().get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecc062cb",
   "metadata": {},
   "source": [
    "Let's do some rotations on y-axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "57d9a0c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=183x70 at 0x7F2C39C13460>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(1, 1)\n",
    "qc.ry(-pi/4, 0)\n",
    "\n",
    "qc.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "fd41e7af",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results from z measurement: {'1': 141, '0': 883}\n",
      "Results from x measurement: {'0': 120, '1': 904}\n"
     ]
    }
   ],
   "source": [
    "for basis,circ in [('z', meas_z), ('x', meas_x)]:\n",
    "    print('Results from ' + basis + ' measurement:',\n",
    "      backend.run(qc.compose(circ)).result().get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44f3c1ea",
   "metadata": {},
   "source": [
    "## Unique quantum correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2882a291",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=544x103 at 0x7F2C39C13A60>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_charlie = QuantumCircuit(2,2)\n",
    "qc_charlie.ry(1.911,1)\n",
    "qc_charlie.cx(1,0)\n",
    "qc_charlie.ry(0.785,0)\n",
    "qc_charlie.cx(1,0)\n",
    "qc_charlie.ry(2.356,0)\n",
    "qc_charlie.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1d0d4f41",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=219x132 at 0x7F2C39C1E1F0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "meas_zz = QuantumCircuit(2,2)\n",
    "meas_zz.measure([0,1],[0,1])\n",
    "meas_zz.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c956e7d8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results for z measurements:\n"
     ]
    },
    {
     "data": {
      "image/png": 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UPcSrgA9m5heBfa3alwF1XVaVJEllVmogng6saKf9NaDf0ZcjSVJllBqI64Bp7bRfAKw6+nIkSaqMUkeZfgGYGxEnUziHOCMi3g9cD1zR1cVJklQupc5D/FpEVAGfBU6mMEn/BeDDmfnNbqhPkqSyOJJ5iPOAeRExGDghM7d1fVmSJJVXyYG4X2a+2JWFSJJUSYcNxIj4BTA7M3dExLNAdtQ3M6d0ZXGSJJVLZ/YQHwSaWz3uMBAlSTpWHTYQM/NTrR7f1K3VSJJUIaVeuu3JiHhDO+39I+LJLqtKkqQyK3Vi/nlA33baTwLOPepqJEmqkE6NMo2I1lenmRIR21s97wO8DWjqysIkSSqnzk67aKQwmCaBx9tZvge4rquKkiSp3DobiKMpXKptHfAnwG9bLXsV2JaZLV1cmyRJZdOpQMzMDcWHJd9QWJKkY0FnJua/E/heZr5WfNyhzPy3LqtMkqQy6swe4reBYcC24uOOJIUBNpIkHXM6MzH/hPYeS5LUmxhwkiTR+XOIneI5REnSsaqz5xA7w3OIkqRjVknnECVJ6q0MO0mScB6iJEmA8xAlSQKchyhJEuA5REmSgCMIxIiYFhH3RkRj8ee+NvdLlCTpmFNSIEbEe4GfAacCPyj+DAWejoj3dfI1romI9RGxNyKWRsS5h+j7zoh4PCJ+GxG7ImJJRFxYSs2SJHVGqXuInwE+kZnnZ+aNxZ8/Az4BfPpwK0fEJcAXgc8CZwFPAY9GxGkdrDIbeBL482L/HwAPHSpEJUk6EqUG4huB/9tO+7eAIZ1Yfw5wd2bOy8xfZuZ1wGbg6vY6Z+ZHMvNzmfl0Zv46Mz8FLAX+ssS6JUk6pE7dILiVHwPnAb9u034esOBQK0ZEX+Bs4AttFj0OvLmEGk4BdnTwO64ErgSora1l/vz5AIwZM4ZTTjmF5cuXAzBo0CDq6upYuHAhAFVVVcycOZNly5axc+dOABoaGti6dSswtoTSji/PP/8869atA2DUqFEMHDiQZcuWATBgwADq6+tZsGABmUlEMHv2bJYvX86OHYWPb9q0aWzfvp3nnnsOOLrPaePGjQCMGzeO6upqVqxYAcCQIUMYP348ixYtAqC6upoZM2bQ2NjI7t27AZg+fTqbNm2iqakJgAkTJtCnTx9WrVoFwLBhwxg9ejSLFy8GoF+/fkyfPp0lS5awZ88eAGbMmMH69evZsmVL8a9zXtf+sXuR+fPn95jPaeLEibS0tLB69WoAhg8fzogRI1iyZAkANTU1NDQ0sHjxYpqbmwGYOXMma9asYdu2bQBMmjSJ5uZm1q5dC8DIkSMZOnQojY2NAPTv359p06axaNEi9u3bB8CsWbNYuXIlL730EgD19fXs2rUL6OhgmTZv3twln9OhRGYeusPBk/FPBW4CHgT+X7HtTcA7gZsy845DvE4t0ATMzsyFrdpvBN6bmRMOWUih77XA54BJmbnhUH0bGhpy/wZ5ND54+1G/RK8176OVrqDncrvpmNtNx9xuOtZV201ELM3MhvaWHenFvQ/sibXyz0CHgXi0IuKvgM8DlxwuDCVJKlU5L+79ItBCYVRqa0OBLa/v/gcR8S7gXuCyzPxeF9UjSdIBZZuYn5mvUhgQc36bRedTGG3aroi4GLgPuDwzO3srKkmSSlLqoBoiYgDwDgpnf/u2XpaZNx9m9duA+yLiaeCnwFVALXBn8bXvLb7OZcXnl1IIw48BCyNiWPF1Xs3M7aXWLklSR0oKxIh4E/AI0ExhCkYThYE2zcBzwCEDMTO/GRGDgBuK660ALmh1TrDtEKurijXeXvzZbwEO45MkdaFS9xA/D/wr8BFgJ/CnwMvA/cBXO/MCxZGo7Q6+yczzDvVckqTuUuo5xCnA3CzM1WgBqjNzK/BxCtMxJEk6JpUaiK+2erwVOL34eDeFc4GSJB2TSj1kugw4B1gDzAc+HRFDgfcBv+ja0iRJKp9S9xD/AXih+PgG4LcUJuQP4PUT9SVJOmaUtIeYmY2tHv+WwvQLSZKOeSXPQwSIiLHAmcWnqzJzXdeVJElS+ZU6D3EQhekVFwK//0NzfB+4IjNf6uL6JEkqi1LPIf5v4AzgXOCk4s8sYDQwr2tLkySpfEo9ZPo24D9n5uJWbT+NiP8O/LDrypIkqbxK3UP8LYUr07T1CuDhUknSMavUQLwZuD0ihu9vKD7+Jw5zHVNJknqywx4yjYhngWzVNBp4LiKais+HA3uBIRTOMUqSdMzpzDlE70EoSer1DhuImfmpchQiSVIlHenE/D8FJlI4lLoyM+d3ZVGSJJVbqRPzhwMPAWfzh2ua1kZEI3BRZr7Q4cqSJPVgpY4y/RKF+yCekZkjM3MkMK7Y9qWuLk6SpHIp9ZDp+cB5mbl+f0NmrouIDwM/6tLKJEkqo1L3EOHgKRiHapMk6ZhRaiD+CPjniBi5vyEiTgNuxz1ESdIxrNRA/DDwR8C6iNgQERuA3xTbPtzVxUmSVC6lnkN8CfgT4Dzgj4ttv8xML+wtSTqmdToQI6IP8B9AfWY+ATzRbVVJklRmnT5kmpktwAagb/eVI0lSZZR6DvF/Ap+LiMHdUYwkSZVS6jnEj1G420VTRGyizb0RM3NKVxUmSVI5lRqI36Yw5zC6oRZJkiqmU4EYEScDnwf+EjiRwpzD6zLzxe4rTZKk8unsOcRPAZcDjwD3A28FvtJNNUmSVHadPWT6TuADmfkAQET8K/DTiOhTHH0qSdIxrbN7iCOBn+x/kplPA/uA2u4oSpKkcutsIPYBXm3Tto8jvMGwJEk9TWcDLYCvR0Rzq7aTgHkR8cr+hsy8sCuLkySpXDobiPe00/b1rixEkqRK6lQgZubfdHchkiRV0pHcIFiSpF7HQJQkCQNRkiTAQJQkCTAQJUkCDERJkgADUZIkwECUJAkwECVJAgxESZIAA1GSJMBAlCQJMBAlSQIMREmSAANRkiTAQJQkCTAQJUkCDERJkgADUZIkwECUJAmoQCBGxDURsT4i9kbE0og49xB9T42Ib0TEryKiJSLuLmOpkqTjSFkDMSIuAb4IfBY4C3gKeDQiTutglWrgReBzwJKyFClJOi6Vew9xDnB3Zs7LzF9m5nXAZuDq9jpn5nOZ+eHMvBvYXsY6JUnHmbIFYkT0Bc4GHm+z6HHgzeWqQ5Kk9lSV8XcNBvoAW9u0bwXe2hW/ICKuBK4EqK2tZf78+QCMGTOGU045heXLlwMwaNAg6urqWLhwIQBVVVXMnDmTZcuWsXPnTgAaGhrYunUrMLYrSuuVnn/+edatWwfAqFGjGDhwIMuWLQNgwIAB1NfXs2DBAjKTiGD27NksX76cHTt2ADBt2jS2b9/Oc889Bxzd57Rx40YAxo0bR3V1NStWrABgyJAhjB8/nkWLFgFQXV3NjBkzaGxsZPfu3QBMnz6dTZs20dTUBMCECRPo06cPq1atAmDYsGGMHj2axYsXA9CvXz+mT5/OkiVL2LNnDwAzZsxg/fr1bNmypfjXOa9r/9i9yPz583vM5zRx4kRaWlpYvXo1AMOHD2fEiBEsWVI4Q1NTU0NDQwOLFy+mubkZgJkzZ7JmzRq2bdsGwKRJk2hubmbt2rUAjBw5kqFDh9LY2AhA//79mTZtGosWLWLfvn0AzJo1i5UrV/LSSy8BUF9fz65du4COzh5p8+bNXfI5HUpkZje+hVa/KKIWaAJmZ+bCVu03Au/NzAmHWf/7wIuZeXlnfl9DQ0Pu3yCPxgdvP+qX6LXmfbTSFfRcbjcdc7vpmNtNx7pqu4mIpZnZ0N6ycp5DfBFoAYa2aR8KbHl9d0mSyqdsgZiZrwJLgfPbLDqfwmhTSZIqppznEAFuA+6LiKeBnwJXAbXAnQARcS9AZl62f4WImFp82B/4ffH5q5m5qnxlS5J6u7IGYmZ+MyIGATcApwIrgAsyc0OxS3tnlH/e5vlfABuAUd1VpyTp+FPuPUQy8w7gjg6WnddOW3R3TZIkeS1TSZIwECVJAgxESZIAA1GSJMBAlCQJMBAlSQIMREmSAANRkiTAQJQkCTAQJUkCDERJkgADUZIkwECUJAkwECVJAgxESZIAA1GSJMBAlCQJMBAlSQIMREmSAANRkiTAQJQkCTAQJUkCDERJkgADUZIkwECUJAkwECVJAgxESZIAA1GSJMBAlCQJMBAlSQIMREmSAANRkiTAQJQkCTAQJUkCDERJkgADUZIkwECUJAkwECVJAgxESZIAA1GSJMBAlCQJMBAlSQIMREmSAANRkiTAQJQkCTAQJUkCDERJkgADUZIkwECUJAkwECVJAgxESZIAA1GSJMBAlCQJMBAlSQIMREmSAANRkiSgAoEYEddExPqI2BsRSyPi3MP0n13stzci1kXEVeWqVZJ0/ChrIEbEJcAXgc8CZwFPAY9GxGkd9B8N/KDY7yzgFuCfI+KvylOxJOl4Ue49xDnA3Zk5LzN/mZnXAZuBqzvofxXwQmZeV+w/D7gH+FiZ6pUkHSciM8vziyL6Aq8A787Mb7Vq/zIwKTNnt7POQuDZzLy2VdtfA98ATs7M19r0vxK4svh0ArC6y99I5Q0GXqx0ETrmuN3oSPTG7eb0zHxjewuqyljEYKAPsLVN+1bgrR2sMwz4YTv9q4qvt7n1gsz8F+BfjrrSHiwiGjOzodJ16NjidqMjcbxtN44ylSSJ8gbii0ALMLRN+1BgSwfrbOmg/z563268JKmCyhaImfkqsBQ4v82i8ymMIm3P4g76N7Y9f3gc6dWHhNVt3G50JI6r7aZsg2rgwLSL+4BrgJ9SGEX6AaAuMzdExL0AmXlZsf9oYAUwD7gLeAtwB4WBOQ+WrXBJUq9XzkE1ZOY3I2IQcANwKoWwuyAzNxS7nNam//qIuAD4XxSmZrwAfNgwlCR1tbLuIUqS1FM5ylSSJAxESZIAA1Hq1SIiWv9XUsc8hygdR/YHY/oPX3qdso4yVWkiol9m7ql0HTr2RMQJwH8F3gicDDQBCzJzW0ULk3ow9xB7qIgYACwHHgG+Djy1/1t9RESrx39M4Y4gOytWrHqUiDgF+Crwn4DfA5uABPYCC4D7MvNXrbcjKSJOBEYDGzKzudL1VILnEHuu91G4TN3ZwELg1xFxc0RMaBWGI4H7KVzoXNrvwxTu9nJBZg4F3gvcDjwL/BnwjxHxRsNQbVwL/By4MyL+IiKGRUSf1h0ion9EvKMYnr2Oe4g9VETMo3Dt1xsp3PXj3cC7gDHAz4D/AwwC/iEzaypVp3qeiPgJ8FBm3tamvQ+Fqz19FfhNZr69EvWpZ4qIxRSOIlQBbwaeBx4C/o3Cbfj+IyKuAi7PzDdVrtLu4x5iDxQR1cAqYGNmbsvMX2Tm/wAagLcVl90EfAa4tWKFqseJiCoKV4D6q4h4Y7GtT0SckJktmbmQwiUTR0REfSVrVc9R3FZeA+Zl5rnA6RS+OP0XCkeonoyIjwMfBZZUqs7u5h5iD1UMxQGZuaX4zT4z8/etlp8HPAmclpmbKlOleqKIeBPwr8C3gdsyc2ub5SOBXwITMrOpAiWqh4mIU4FLgVWZ+e9tlp0F/G1x+QBgZG/dbgzEHmj/YIeIGAO83Pp/aK2W3Ujh0MWYylWqnqY4uvQE4G+Az1I4/PUg8E0Kh8CmUPjWPzEzz6lUnep5IqIfhS/ee1vPW201ZuEzFM5Ln1WpGrubgdjDRMQQ4P3AHGAbhXs/bga+BfxbZr5c3Fg/SGF06fcrVqx6tIh4A3A58B5gKrCLwjminwG3ZGavPfSlI9PRyOOIOBlYBnwtM3vtaRoDsYeJiLuBOuB7wHZgIHAW8McUhs9/PjMfr1iB6rEioj+wq/X/0Ip7jCcBNcAkCkccDEId0N52006fk4BLgPuL97btlQzEHqS457eLwmGJha3aRgBvorBXeDqF+0Euq1ih6pEi4i7g6eLPhvbmpkbEgMzc4RxE7dfJ7eYNmfm7ctdWbo4y7VkmAuuBA9/AsmBjZn6LwrmfXcBfV6g+9VAR8W4KX5j+Cfgu8PmIeGdEnFE8N0RE1ABfi4jJhqGgw+3moogY22q76QfcExGTKlhqWbiH2IMUN7zvU7jU1mUU5or9vk2f64APZObU8leonqrVvNV/BN4J/DdgLLAa+AHwIwqT9b+YmX0rVad6FrebgxmIPUxxyPydwB7gLgob5I7M3F08sX0vsDcz31fBMtWDFOceXg/0z8y/b9VeR+Hb/7sonEd8A3BPZn6gEnWqZ3G7eT0DsQcqHpr4BHAh8DKwGPgt8FYKI07/NjOfrVyF6mmK174dWrxGaV/gtTaDay6hcJm/aZn5TIXKVA/jdnMw73bRA2XmCuCS4hSMPwf+EvgjYB7wrcz8VQXLUw+UmTuAHcXHr8KBEaaRmS1AfwpHFp6pWJHqcdxuDuYe4jGieOmt3x++p/R6ETEH6JOZn690LTp2HG/bjYEoHQeKdydo8UuVSnG8bTcGoiRJOA9RkiTAQJQkCTAQJUkCDERJkgADUZIkwECUJAmA/w/h9VemoHldfQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Results for z measurements:')\n",
    "counts = backend.run(qc_charlie.compose(meas_zz)).result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5989d7a5",
   "metadata": {},
   "source": [
    "(Observation A) Never found 00 from zz measurement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fe1fa51d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMYAAABjCAIAAABPKOhXAAANWklEQVR4nO2dfUwTZxzHH+rxYstEp2O8WzBsqS2OLCKC4DpANFMWpgIaBwZjsug0MQLLBgGMEzaD4w8dc9mSOXQOpnshc3MLgwIriLwmClNkhMK0FEaFYo+sLW2f/XGmY9D3Xu965fn81Tue5/l9+/Dtc8/dPfc7DwghQDgTT09PrVZLWTgMw+bm5igLtxgPZCln4+FBaSdTHG4xGI2xycIZwwDtv3Xm4g6W0mq1pP8uPTw8yG1w6cCiWwDCTr7++mu1Wk23CiMgSzGS27dvv/vuu3SrMA6yFCPJz88/c+aMt7c33UKM4A5zqcUolcq///7by8uLxWJBCHU6HYSQy+XOzs7KZDJvb29iqqTT6XQ6XUREBN16beP69es4jr/55pt0CzHOf6MUhPDhw4cajYbYNHxgIuPj4zU1NYcOHQoJCVm/fv3FixdFIhEAQC6X19bWvvXWW6GhoZGRkVVVVfX19XSLtQ2NRlNUVHTu3DkWy1WPMBBCCGFra+uuXbsuXbpUWlra2Nh45MiRhoYGaCMqlSoxMfHYsWO2VnQQw7dYQHd3NwBg165dC/YPDAwAAIRCoR1tkijPPiorK9PS0igLZwcAQvjdd99FRkZOTEwQuzIzMz09PWdnZ21ta2JiwsvLSyAQkKzREqY6sb+/HwCwd+/eBftHRkYAADt27LCjTRLl2cHU1JS/v39/fz814ewDGx8fz83Nraqq8vf3J8YtNpu9adMmNpsNAOju7v711185HA6fz09NTTU/4Pn7+0skkmeeecYZoykCAHDmzJk9e/bw+Xy6hZgDKy4u1uv1GRkZhl1isTgrKwsA0Nvbe/bs2ZqaGgzDSktLe3p63nvvPfPNBQUFOVfvEkYikVRXVxNDr0sTFBS0c+dOw6j18OFDAEB9fT2EMCYmxjCjUqlUfn5+MzMz9AymZgFL48CXkZFRVlZGWTi7wcbGxo4dO2ZwmEgkwjAsPj5eoVB0d3evW7eO2O/t7e3n51dfX793716KTe8gnZ2d2dnZ8/fgOE6XGCvBcXx2dlaj0fj6+nI4HC8vr46Ojvb29i+//JJuaZbBAACRkZGG7YaGhpiYGA6H09nZCSEkZlQEbDZ7fHzcfHPT09NsNtviJbjw8HBiqKCATZs2XblyZf6e0dHRuro6ixWpvM0nkUhEIlFLS8sff/wxODgIAPD19fXy8lIqlf/8809AQIBCoRAKhbdu3dq6dauXl5f51hxRjmGYI/fguVwuSyAQKBQKYrupqam2tvaVV14BABD3j+aL0+v1MzMzZpp7/PhxaGhoQkKCxcASiYTEkdbu728eCuThOF5VVbV58+a4uLjm5ubExMRPP/1UKpUqlUqZTDY6Ojo1NaVUKvPy8latWrV+/frS0tKgoKDDhw/39PQ4Sfnc3Jwj1SUSCfbFF1/k5eWtXr16aGhIr9fPzc0JhUIAwIoVKwAA8w07MzNj/myOzWZHRETweDyb/nNLk9nZ2YqKik8++eTVV189ffp0cnLysmXLjJbU6/Xnz5//7LPPUlJSAACPHj2qqanZs2dPeHh4WVlZfHw8tcKtAEKoUqn6+vrUavXly5cxDFMqlRBCtVrt4+Nz584dgwG9vb3FYrEjFnYSgGnT82+//TYsLCwnJ2doaMhi9Y8++mjxtc25ubnq6urQ0NADBw5MTk6aD0cx/wt/6NCh2NhYw+bBgwcvXbpEfB4eHn7xxRfVajWV4qyEQZbCcTw3N5fH47W2tlpT1/y1TRzHCwoKgoODf/vtN6PhaOG/8Dqdbu3atfn5+YY909PT27dv/+GHH1pbW3fv3k1M2F0QU53Y1tYGAEhNTV2w/86dOwCAuLg4O9p0RJ5UKt2wYUNubi6O41bWPXny5JEjR8yXaWxsDA4OvnDhwoJwdPE0fElJiVAo9PT05PP5J0+eNPxZq9V2dXX9/vvvxNHQNVnciT09PTk5OTExMX5+fmvWrNm3b19xcTGEsL+//+DBg5s3b/bz81u1alVmZmZBQYGVbTooTyKRhIeHf/jhh9ZXHB4eXrNmjUwms1hyZGSEx+NVVFRAF7DU06XvWq0Ww54udJn/mRE4YwE/iW0STQ0MDNy7d2/37t3WV8zMzIyOji4sLLSmsEKhGB0dfemll2h/nMEdnpBhhKVsrTU0NJSUlPTgwYPly5dTEI5EkKWc3qZ9TUEIp6enn332WWrCkQiylNPbXGrP8bnqykAEY0GWQpAMk87sTIFhGOm3eJl1zutSuEPHufiT5s5wvPlwlMUyijtMz92P+VNs2qfbtoLmUgiSQZZCkAyyFIJkGDk9X2p55ZgFIy3ljIRSZkC5pmwCHfgQJIMs9R99fX10S3AHkKWe0t7enpaWRrcKdwBZ6ikFBQXvv/8+3SrcAWQpAAC4fv367OzsgQMH6BbiDrhnyjKb0Gg0hYWFFRUVrpsEjFE87cS2trbXX3+9sbGxvLxcJBIdPXpULBbb2pZard66devx48fJFulcPv74Yx6PRzx4iSAByMCUZcDdk4DNj0h9dAdhESnLSkpKjKYsAwCMj4+Xl5db404iZdmtW7ecYX0nwYgkYAzj8OHDvr6+KpXK4LJ169YVFhZCCNvb24uKinJycrhcLn2mNwIg6Ydr5YNyZIWzHsDkUcpcyjKCuro6d7WUyyYBY7SlWGNjY1u2bDEMWoaUZdSPlxRDJAE7ceIE3ULcDZMpy+xrznVSlmm12t7eXrFYfP/+/cHBwcnJSRzH9Xq9j4/Pc889FxER0dbWtn//fp1OZ01r1N859vDwMGQPo3idsYMpy7DFKcvy8vLsa+7x48dr167l8XhdXV3mS0okEvtCEJjpYghhc3PzlStX6urqQkJChEJhbGxsdnZ2QEAAh8NhsVgqlWpycvLq1asqlaqjoyMkJCQxMTErKysjI8PHx8dMs44IthVGLxQ2mbLMDuhNWabX67/55puzZ89CCHNzc8vKygIDA42WDAkJyc7Ovnr1akpKCo7jN27c+Oqrr955552jR4+eOHECJdl2FGgiZZkBRkzPu7u7Y2Nj4+LifvnlF71eb7660Rcc3Lt3Lzs7Ozg4uLq62mI4ZwOYPD03l7KM4Pvvvw8LC6NQkmXm97JWqz19+nRgYGB1dbVFM0FL1zY7Ojpefvnl9PR0uVxuNBw1uImlFqcsu3//fklJSXJy8sqVK/Py8iorK+lQaARDLysUipSUlOTk5LGxMSvrWkwCplarCwoKwsLC+vr6FoSjDHewlKmUZa4J0csymSw6Ovr48ePEu9GsYXh4ePXq1dYkAautrX3++eeJ9IfIUjbByJRlxElQXV3d0NBQfn6+9RWzsrI2bNhQVFRkTeG2tja1Wp2UlET9ORejz/gYJpfAvl7u7e1NT08fGBiY/34A54VzBGQpqrGvl+VyuUwmi4qKoiacIyBLUY3bJwFjtKXQOkYEySBLIUgGWQpBMshSCJJx6etPplhqeeWYBcPOJuyGWedQzFK7AHTgQ5AMshSCZJClECSDLIUgGWQpBMkgSyFIBlkKQTJuaym9Xn/q1CkzV3QghKdOndLr9VSqMgWz1JrHbS3FYrGePHnywQcfmCpQXl6uVCpdJKcUs9RagJLlyPSg0WgSEhKam5vhotXcTU1NCQkJGo2GPnULYZZaM7izpSCEo6OjAoFgYmJiwT9JIBD89ddfNAozCrPUmsJaS/35559NTU2GtGYM4qefftq2bZvh6Va9Xr98+fKff/6ZXlWmYJZao1g+Nre0tMTExIhEIgDAxYsXi4uLTU0SXTOx4s6dO4ODgy9cuEBs3rhxY9++fa+99hq9qkzBLLXGMe+4lpYWDMN6e3uJzbq6Og6H09DQYLQwZYkVbeXBgwdbtmwhPsfHxw8ODtKrxzzMUrsYC5bi8/k7duwwbDY0NERHRw8MDJgqL5VKnzx5YjEql8ul5fezbNkyWuLaBy1qHVwcxuVyzVmKyIiXl5dn0SKuz927d7dt25aSknL37l26tViGWWoXYM6SQ0NDAICAgABHbOsiREVFqVQqFotlx3N81MMstQswZykiOx4xVrkB586dY9Br0Jil9n+YH8SioqISExPn71Gr1T/++KOp8lNTU/OTE5uCrrkUs1aR06LWuXMpCOHt27cxDLt586Zhz/nz57u6uowWlsvlHA5n48aNFi2FcGMsWDI2Nra1tfXtt99ua2sjzvX4fP7GjRuNFqY3sSLCRbD26YuJiQmFQvHCCy8w9QCPoAqGPdCDcH2YsFgCwSiQpRAkgyyFIBlkKQTJMOnSn91IJBKxWPz5559fu3bN1CsbXIfx8fFr164FBARMTk6mpaWFhYXRrchG6L4wRgVjY2MymUwgEIyMjNCtxTKpqalSqRRCKJfLk5KS6JZjM0viwBcYGMiUm99TU1NdXV1BQUEAAOLFPo8ePaJblG0sCUsxCKlUumLFCsPmypUrkaUQDuHr64vjuGETx3FfX18a9dgBspRrER4ezuFwNBoNAIB4yxLj7pkuiRsyvb29jY2NlZWV+/fvj4uLy8jIoFuROerr6zs7O994442bN29GRkamp6fTrcg2/gVOi6VPvWPx5AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=198x99 at 0x7F2C385C2E80>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "meas_zx = QuantumCircuit(2,2)\n",
    "meas_zx.h(0)\n",
    "meas_zx.measure([0,1],[0,1])\n",
    "meas_zx.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "9deecd34",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results for a z and an x measurement:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Results for a z and an x measurement:')\n",
    "counts = backend.run(qc_charlie.compose(meas_zx)).result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "8b36388e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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E2Fy0tWvXDg4OjoyMEC3KFP7+/vjP2LMt0OV4Mzo6urRh9tRTT5Hc5U4AdDneeHp6KpVK3aZSqXSaVBykBbocbzZu3Ein0zUaDYIg2CvDK5z5AzELicZYVg+1tbWdnZ0HDx6srq5msVgvvfQS0YpM0d3dLRQKP/3004yMjB07dqSlpRGtaNn8AySWfwgeHcMyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=247x99 at 0x7F2C385854F0>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "meas_xz = QuantumCircuit(2,2)\n",
    "meas_xz.h(1)\n",
    "meas_xz.measure([0,1],[0,1])\n",
    "meas_xz.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d532f8ea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results for an x and a z measurement:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Results for an x and a z measurement:')\n",
    "counts = backend.run(qc_charlie.compose(meas_xz)).result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05ea6433",
   "metadata": {},
   "source": [
    "(Observation B) never found 11 in either xz or zx measurement"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20e0179c",
   "metadata": {},
   "source": [
    "By logic*, we shouldn't find 11 in an xx measurement. Let's find out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a2ef5999",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=247x99 at 0x7F2C38559970>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "meas_xx = QuantumCircuit(2,2)\n",
    "meas_xx.h([0,1])\n",
    "meas_xx.measure([0,1],[0,1])\n",
    "meas_xx.draw('latex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "56585bf9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results for an x and an x measurement:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Results for an x and an x measurement:')\n",
    "counts = backend.run(qc_charlie.compose(meas_xx)).result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9139e01d",
   "metadata": {},
   "source": [
    "The results of qubits are not well-defined before measurement. Though this might seem like it means that qubits are more random that classical variables, it is not always a negative quality. It also means that restrictions applied to classical variables do not always apply to qubits, and that quantum correlations can have properties that would be impossible classically. These unique correlations are one of the signature properties of entangled states.<br>\n",
    "(Words taken from Qiskit textbook)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "519bcea4",
   "metadata": {},
   "source": [
    "*explanation:<br>\n",
    "from observation A: there's no way for both qubits to be in state 0<br>\n",
    "from observation B: if one qubit is measured 1, the other must be 0:\n",
    "* if measured x of a qubit is 1, the other z must be 0\n",
    "* if measured z of a qubit is 1, the other x must be 0<br>\n",
    "\n",
    "from the first point, if both qubits x-measurement yield 1, then the z-measurement from both qubits must yield 0, which violates observation A."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.10 64-bit",
   "language": "python",
   "name": "python3810jvsc74a57bd0916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
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 },
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}