terra/qis_intro/entanglement_testing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://raw.githubusercontent.com/Qiskit/qiskit-tutorials/master/images/qiskit-heading.png\" alt=\"Note: In order for images to show up in this jupyter notebook you need to select File => Trusted Notebook\" width=\"500 px\" align=\"left\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## _*Testing Entanglement*_ \n",
    "\n",
    "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorial.\n",
    "\n",
    "\n",
    "***\n",
    "### Contributors\n",
    "Jay Gambetta, Antonio Córcoles, Anna Phan\n",
    "\n",
    "### Qiskit Package Versions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'qiskit': '0.10.3',\n",
       " 'qiskit-terra': '0.8.1',\n",
       " 'qiskit-ignis': '0.1.1',\n",
       " 'qiskit-aer': '0.2.1',\n",
       " 'qiskit-ibmq-provider': '0.2.2',\n",
       " 'qiskit-aqua': '0.5.1'}"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import qiskit\n",
    "qiskit.__qiskit_version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Entanglement\n",
    "\n",
    "In [creating entanglement](entanglement_introduction.ipynb), we introduced you to the quantum concept of entanglement. We made the quantum state $|\\psi\\rangle= (|00\\rangle+|11\\rangle)/\\sqrt{2}$ and showed that (accounting for experimental noise) the system has perfect correlations in both the computational and superposition bases. This means if $q_0$ is measured in state $|0\\rangle$, we know $q_1$ is in the same state; likewise, if $q_0$ is measured in state $|+\\rangle$, we know $q_1$ is also in the same state.\n",
    "\n",
    "To understand the implications of this in more detail, we will look at the following topics in this notebook:\n",
    "* [Two-Qubit Correlated Observables](#section1), where we learn more about two-qubit observables\n",
    "* [CHSH Inequality](#section2), where we use the observables to compare quantum mechanics to hidden variable models on two qubits\n",
    "* [Two-, Three-, and Four-Qubit GHZ States](#section3), where we create entangled states over more qubits\n",
    "* [Mermin's Test and the Three Box Game](#section4), where we compare quantum mechanics to hidden variable models on three qubits\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Two-Qubit Correlated Observables<a id='section1'></a>\n",
    "\n",
    "An observable is a Hermitian matrix where the real eigenvalues represent the outcome of the experiment, and the eigenvectors are the states to which the system is projected under measurement. That is, an observable $A$ is given by\n",
    "  \n",
    "\n",
    "$$  A = \\sum_j a_j|a_j\\rangle\\langle a_j|$$ \n",
    "\n",
    "where $|a_j\\rangle$ is the eigenvector of the observable with result $a_j$. The expectation value of this observable is given by \n",
    "\n",
    "$$\\langle  A \\rangle  = \\sum_j a_j |\\langle \\psi  |a_j\\rangle|^2  = \\sum_j a_j \\mathrm{Pr}(a_j|\\psi).$$\n",
    "\n",
    "We can see there is the standard relationship between average (expectation value) and probability. \n",
    "\n",
    "For a two-qubit system, the following are important two-outcome ($\\pm1$) single-qubit observables:  \n",
    "\n",
    "$$ Z= |0\\rangle\\langle 0| - |1\\rangle\\langle 1|$$ \n",
    "$$ X= |+\\rangle\\langle +| - |-\\rangle\\langle -|$$ \n",
    "\n",
    "These are also commonly referred to as the Pauli $Z$ and $X$ operators. These can be further extended to the two-qubit space to give \n",
    "\n",
    "$$\\langle  I\\otimes  Z\\rangle =\\mathrm{Pr}(00|\\psi) - \\mathrm{Pr}(01|\\psi) +  \\mathrm{Pr}(10|\\psi)- \\mathrm{Pr}(11|\\psi)$$ \n",
    "$$\\langle  Z\\otimes  I\\rangle =\\mathrm{Pr}(00|\\psi) + \\mathrm{Pr}(01|\\psi) -  \\mathrm{Pr}(10|\\psi)- \\mathrm{Pr}(11|\\psi)$$ \n",
    "$$\\langle  Z\\otimes  Z\\rangle =\\mathrm{Pr}(00|\\psi) - \\mathrm{Pr}(01|\\psi) -  \\mathrm{Pr}(10|\\psi)+ \\mathrm{Pr}(11|\\psi)$$ \n",
    "\n",
    "$$\\langle  I\\otimes  X\\rangle =\\mathrm{Pr}(++|\\psi) - \\mathrm{Pr}(+-|\\psi) +  \\mathrm{Pr}(-+|\\psi)- \\mathrm{Pr}(--|\\psi)$$ \n",
    "$$\\langle  X\\otimes  I\\rangle =\\mathrm{Pr}(++|\\psi) + \\mathrm{Pr}(+-|\\psi) -  \\mathrm{Pr}(-+|\\psi)- \\mathrm{Pr}(--|\\psi)$$ \n",
    "$$\\langle  X\\otimes  X\\rangle =\\mathrm{Pr}(++|\\psi) - \\mathrm{Pr}(+-|\\psi) -  \\mathrm{Pr}(-+|\\psi)+ \\mathrm{Pr}(--|\\psi)$$ \n",
    "\n",
    "\n",
    "$$\\langle  Z\\otimes  X\\rangle =\\mathrm{Pr}(0+|\\psi) - \\mathrm{Pr}(0-|\\psi) -  \\mathrm{Pr}(1+|\\psi)+ \\mathrm{Pr}(1-|\\psi)$$ \n",
    "$$\\langle  X\\otimes  Z\\rangle =\\mathrm{Pr}(+0|\\psi) - \\mathrm{Pr}(+1|\\psi) -  \\mathrm{Pr}(-0|\\psi)+ \\mathrm{Pr}(-1|\\psi)$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:13:39.306577Z",
     "start_time": "2018-09-29T01:13:37.799759Z"
    }
   },
   "outputs": [],
   "source": [
    "# Imports\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "\n",
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, execute\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "from qiskit.quantum_info.analyzation.average import average_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the best backend is ibmqx2\n"
     ]
    }
   ],
   "source": [
    "from qiskit import IBMQ, BasicAer\n",
    "from qiskit.providers.ibmq import least_busy\n",
    "IBMQ.load_account()\n",
    "\n",
    "# use simulator to learn more about entangled quantum states where possible\n",
    "sim_backend = BasicAer.get_backend('qasm_simulator')\n",
    "sim_shots = 8192\n",
    "\n",
    "# use device to test entanglement\n",
    "device_shots = 1024\n",
    "device_backend = least_busy(IBMQ.backends(operational=True, simulator=False))\n",
    "\n",
    "print(\"the best backend is \" + device_backend.name())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that to make the Bell state $|\\psi\\rangle= (|00\\rangle+|11\\rangle)/\\sqrt{2}$ from the initial state $|00\\rangle$, the quantum circuit first applies a Hadamard on $q_0$, followed by a CNOT from $q_0$ to $q_1$. Using Qiskit, this can done by using the script below to measure the above expectation values; we run four different experiments with measurements in the standard basis, superposition basis, and a combination of both."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:17:22.453706Z",
     "start_time": "2018-09-29T01:17:22.439659Z"
    }
   },
   "outputs": [],
   "source": [
    "# Creating registers\n",
    "q = QuantumRegister(2)\n",
    "c = ClassicalRegister(2)\n",
    "\n",
    "# quantum circuit to make an entangled bell state \n",
    "bell = QuantumCircuit(q, c)\n",
    "bell.h(q[0])\n",
    "bell.cx(q[0], q[1])\n",
    "\n",
    "# quantum circuit to measure q in the standard basis \n",
    "measureZZ = QuantumCircuit(q, c)\n",
    "measureZZ.measure(q[0], c[0])\n",
    "measureZZ.measure(q[1], c[1])\n",
    "bellZZ = bell+measureZZ\n",
    "\n",
    "# quantum circuit to measure q in the superposition basis \n",
    "measureXX = QuantumCircuit(q, c)\n",
    "measureXX.h(q[0])\n",
    "measureXX.h(q[1])\n",
    "measureXX.measure(q[0], c[0])\n",
    "measureXX.measure(q[1], c[1])\n",
    "bellXX = bell+measureXX\n",
    "\n",
    "# quantum circuit to measure ZX\n",
    "measureZX = QuantumCircuit(q, c)\n",
    "measureZX.h(q[0])\n",
    "measureZX.measure(q[0], c[0])\n",
    "measureZX.measure(q[1], c[1])\n",
    "bellZX = bell+measureZX\n",
    "\n",
    "# quantum circuit to measure XZ\n",
    "measureXZ = QuantumCircuit(q, c)\n",
    "measureXZ.h(q[1])\n",
    "measureXZ.measure(q[0], c[0])\n",
    "measureXZ.measure(q[1], c[1])\n",
    "bellXZ = bell+measureXZ\n",
    "\n",
    "circuits = [bellZZ,bellXX,bellZX,bellXZ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:17:26.024157Z",
     "start_time": "2018-09-29T01:17:24.857770Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 541.8x258.86 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bellZZ.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:17:27.287849Z",
     "start_time": "2018-09-29T01:17:26.028739Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 602x258.86 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bellXX.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:17:28.416688Z",
     "start_time": "2018-09-29T01:17:27.290074Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DA+Hh4YGKiop+1dHr9QgNDbV6fH9qJyYmIj8/v1/9kGMZjUY0NTXhqaeestljBgUFwWQyobGx0WaP6WgvvfQS2tvb8e677/Z4BV5PHrz44eDBg8jJyUFMTAxSU1Nx584dO3dM9ADJTlpaWqQnn3xSOnHiRJd5AKQTJ05ItbW1EgCpsrKyy3J+fn7Se++9J0mSJM2dO1fy9vaWXnvttcfuJysrS9JqtZIkSVbV7lBUVCSFh4c/dv2+AODE6ZGnjtd2h7q6OsnV1VV6+eWXrX4NtrS0SHPmzJFcXFy6vA8qKiokANLevXu7jNdqtbI/b07OPfXGbntOxcXFsFgsWLBgQee8W7duAbh/yW7HZyWampq6LGc0GuHh4QHg/knuPXv22Lw3a2p3qKmpgZ+fn817+C5Jkjg94tTW1oYhQ4bgF7/4hVXjrVnf27Ztg6urK1pbW2V/fn1NWq222+vp0KFDMJvN+NnPfmbV6++7e0wPXvwQGhqKGTNmIDs7u9tyWq1W9ufvLJNO/06Ptwfz1Bu7hdPNmzcxcuTILvNyc3MxatQojB49GiqVCn5+figrK+u8v7KyEiaTqfMQna+vr116s6Z2h2PHjiExMdEufZBtDB06FCEhITY9N1haWoqQkBCn/UJYg8GAiRMnYsKECX2O7S2YOjz77LO4dOkS7t69a492ibqxWzhNnjwZV65cQXFxMdrb25Gbmwu9Xg+NRtM5JiUlBenp6aiqqoLJZIJOp0NcXBzGjx9vr7b6VbulpQVnzpxBfHy83fuhxzNr1ix8+umnNvls0p07d1BcXIxZs2bZoDN5XLx4sct77WGsCSbg/tEOSZJw+fJlW7dK1CO7hVNkZCS2b9+O5557Dr6+vjAYDIiKiuryhklLS0NCQgIiIyMxduxYmM1m5OTk9LvWrl27MGXKlH4tY03tU6dOQaPRwNvbu989kWOtX78era2tyMzMfOzH+tOf/oTW1lasX7/eBp3JIykpCYsWLepz3IsvvmjV55iefvpprFu3DiqVypZtEj2c5ED+/v5SXl5ev5bJysqy+QUR1lq9erW0Z8+ex65NjjF//nzJ3d1dqq6u7nVcby/76upqyd3dXYqLi7N1e3aj1Wr7/druUF1dLX344YcOrzsY6fTv9Hibeuaw79YzmUyoqamx6lBDhzVr1sBgMKCtrQ0GgwHHjx+3Y4fd+fv7d34mi8T39ttvIyQkBMnJyTh9+jSGDx/er+Xv3bvX+WHTt99+2x4tCsff3x/+/v5yt0HUjcPC6dKlS1AqlQgMDLR6mQMHDtisvlqtxurVq/u1zKuvvmqz+mR//v7+yMrKwrJly7BgwQLk5eVh1KhRVi1748YN/OhHP8L58+fxwQcfOOS8JxE9nMO+vmjGjBkwmUxQKBSOKtnFo4QTOZ8f/vCHyM3NhcFgwOTJk3HgwAG0tbU9dHxbWxuys7MxZcoUXLhwATk5OdxbJhIAfzKDBpznn38eYWFh+MlPfoK1a9ciLS0NSUlJmDp1auel1QcOHEBJSQmOHDmCmzdvYtq0acjOzkZwcLDM3RMRwHCiASo4OBjnz5/H6dOn8dZbbyE3N7fLeaS1a9dCqVQiJiYGGzZsQGxsbI+/lktE8mA40YDV8TPs8+bNg8ViwZUrV/DNN99Aq9Xi73//OyZOnMhAIhIUw4kGBRcXFwQFBSEoKKjPr00hIvnx30YiIhIO95yIBoDy8nLMnj3b4TXVarVDa9LgwT0nIienVqsfOSQqa6/3eNvedYn6wj0nIie3b9++R142LT0Del1Kt9tEcuOeExERCYfhREREwmE4ERGRcBhOREQkHIYTEREJh+FERETCYTgREZFwGE5ERCQchhMREQmH4URERMJhOBERkXAYTkREJByGExERCYfhREREwmE4ERGRcBhOREQkHIYTEREJh+FERETC4c+0ExHZ2F//9yL+WX2t2/wDeSe73fZ+0hP/EzvDYb05C4YTEZGNPRXoh5PFBlgsUpf5/6iq63Z7evhkh/bmLHhYj4jIxkaOUGG6Zkqf4yaNH4unA/0c0JHzYTgREdnB3JnhGO427KH3KxQKxMdMh0KhcGBXzoPhRERkB8P/2w3Pzpr60Puj1MEY5fOkAztyLsKFk9lsxtatW+Hj4wOlUomkpCQ0NDQM+NpENPBMUwdj5AivbvPdhg3Fs9EPDy4SMJz0ej3y8/NhMBhQX18PAFi5cuWAr01EA4+riwviY57pNj92ZgSeGO4mQ0fOQ7ZwOnfuHObOnQsPDw+oVCosXboUAJCRkQGdToeAgAB4enpi9+7dKCwsRE1Njd17krM2EQ1MQQHj8FTAuM6/vZ/0xDO8Qq9PsoTTRx99hCVLlmDDhg24efMm6urqsG7dOhiNRtTW1iIiIqJzbGBgIDw8PFBRUdGvGnq9HqGhoVaPt2VtIqIHLYqZDheX+xc+LJrzDIa4usrckfgUkiRJfQ+znZaWFvj7+yMzMxOLFy/ucl9dXR38/PxQWVmJCRMmdM739/fHzp07sWLFCuTk5OAPf/gDAGDXrl2YM2eOTfqyprY9paVn2PXxiYhEo9elPPQ+h38It7i4GAqFAomJid3uUyqVAICmpqYu841GIzw8PGA0GvH666/jwoULuHv3LmJjY1FWVgYXl8ffAeyrtr31tpGI7CUtPaPztffgbbK9e9+24m7Ltxjp3f0CCerO4Yf1Ghoa4OXl1eO1/SqVCn5+figrK+ucV1lZCZPJhNDQUBgMBmi1Wri5ucHb2xtjxoxBdXW1TfrqqzYR0eMY/t9uDKZ+cPieU3h4OKqqqnD8+HEsWrQIJpMJBoMBcXFxAICUlBSkp6djzpw5GDFiBHQ6HeLi4jB+/HicP38eXl7/2bheXl64ffs2AgICbNJbb7XtjYf1SC4Pvvb4OiRH6nVPXZJBdna2FBQUJD3xxBPS6NGjpW3btnXe9+9//1tKTU2VRowYIbm7u0tLliyRbt26JUmSJBUWFkobN27sHLtw4ULp6tWrPdbYuXOnNHny5H711VttooFIp3+nx9tEcnP4BRGPw2g0IiYmBp999hlaWloQExNjs3NORIMRzzmRqJzqW8lVKhU2b96M2bNnAwD27t3LYCIiGoCcKpwAYNWqVVi1apXcbRARkR1xt4OIiITDcCIiIuEwnIiISDgMJyIiEg7DiYiIhMNwIiIi4TCciIhIOAwnIiISDsOJiIiEw3AiIiLhMJyIiEg4DCciIhIOw4mIiITDcCIiIuEwnIiISDgMJyIiEg7DiYiIhMNwIiIi4TCciIhIOAwnIiISDsOJiIiEw3AiIiLhMJyIiEg4DCciIhIOw4mIiITDcCIiIuEwnIiISDgMJyIiEs4QuRsgIsf45tYdNLfc6zb/n9X1Pd4O9B8LF4XCIb0RfZdCkiRJ7iaIyP6+vlqL7A8LrRobFhyI5P+Za+eOiB6Oh/WIBomnAsYhaIJvn+OGDHHFgtlRDuiI6OEYTkSDhEKhwKI5z/R5qO4H08Kg8nB3UFdEPWM4EQ0io3yeRJQm+KH3e7gPhzYqzIEdEfVMuHAym83YunUrfHx8oFQqkZSUhIaGhgFfm8hRYmdOhduwoT3eN187DcOG/peDOyLqTrhw0uv1yM/Ph8FgQH39/SuHVq5cOeBrEznKE8PdEDszott83+/5QD1lkgwdEXUnWzidO3cOc+fOhYeHB1QqFZYuXQoAyMjIgE6nQ0BAADw9PbF7924UFhaipqbG7j3JWZvIkaaHT4HPk55d5iXETOel4yQMWcLpo48+wpIlS7BhwwbcvHkTdXV1WLduHYxGI2praxER8Z//6gIDA+Hh4YGKiop+1dDr9QgNDbV6vC1rE4nO1dUFi2Kmd/4dFhwIf9/RMnZE1JXDw6mlpQU//elPkZGRgaSkJLi5uUGpVCIuLg7Nzc0AAE/Prv/RqVQqmEwmAEBsbCx8fHzw61//utc6aWlpuHjxotV9WVObaCB5KmAcJo335aXjJCSHf0NEcXExFAoFEhMTu92nVCoBAE1NTV3mG41GeHh4AACys7Nx+vTpznNCtmJNbXtKS8+wew2ih9G/lSt3CzQI6XUpD73P4eHU0NAALy8vKHo4tq1SqeDn54eysjKo1WoAQGVlJUwmU+chOl/fvj9E+CisqW1PvW0kInuSJKnH9yORnBx+WC88PBxVVVU4fvw4LBYLjEYjioqKOu9PSUlBeno6qqqqYDKZoNPpEBcXh/Hjx9u9NzlrE8mFwUQicvieU0hICDIzM7FlyxYkJydDqVRizZo1iIuLA3D/XFFjYyMiIyPR1taGZ599Fjk5Of2us2vXLhw6dAiXL1+2ehlb1X4UPKxHRINNb0eMnPKLX7Ozs1FfX49XXnlF7laIiMgOnC6c1qxZA4PBgLa2NgQHB+P48eNyt0RERDbmdOFEREQDn3BfX0RERMRwIiIi4TCciIhIOAwnIiISDsOJiIiEw3AiIiLhMJyIiEg4DCciIhIOw4mIiITDcCIiIuEwnIiISDgMJyIiEg7DiYiIhMNwIiIi4TCciIhIOAwnIiISDsOJiIiEw3AiIiLhMJyIiEg4DCciIhIOw4mIiITDcCIiIuEwnIiISDgMJyIiEs7/AQhCVdoH1x74AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 541.8x258.86 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bellZX.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:17:29.721809Z",
     "start_time": "2018-09-29T01:17:28.418497Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 602x258.86 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bellXZ.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:17:35.891126Z",
     "start_time": "2018-09-29T01:17:34.484271Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Job Status: job has successfully run\n"
     ]
    }
   ],
   "source": [
    "job = execute(circuits, backend=device_backend, shots=device_shots)\n",
    "job_monitor(job)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:18:06.919487Z",
     "start_time": "2018-09-29T01:18:06.390647Z"
    }
   },
   "outputs": [],
   "source": [
    "result = job.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:18:06.927728Z",
     "start_time": "2018-09-29T01:18:06.922256Z"
    }
   },
   "outputs": [],
   "source": [
    "observable_first ={'00': 1, '01': -1, '10': 1, '11': -1}\n",
    "observable_second ={'00': 1, '01': 1, '10': -1, '11': -1}\n",
    "observable_correlated ={'00': 1, '01': -1, '10': -1, '11': 1}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:18:07.198423Z",
     "start_time": "2018-09-29T01:18:07.189958Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IZ = 0.044921875\n",
      "ZI = -0.017578125\n",
      "ZZ = 0.41796875\n",
      "IX = 0.220703125\n",
      "XI = 0.166015625\n",
      "XX = 0.50390625\n",
      "ZX = -0.0078125\n",
      "XZ = 0.037109375\n"
     ]
    }
   ],
   "source": [
    "print('IZ = ' + str(average_data(result.get_counts(bellZZ),observable_first)))\n",
    "print('ZI = ' + str(average_data(result.get_counts(bellZZ),observable_second)))\n",
    "print('ZZ = ' + str(average_data(result.get_counts(bellZZ),observable_correlated)))\n",
    "\n",
    "print('IX = ' + str(average_data(result.get_counts(bellXX),observable_first)))\n",
    "print('XI = ' + str(average_data(result.get_counts(bellXX),observable_second)))\n",
    "print('XX = ' + str(average_data(result.get_counts(bellXX),observable_correlated)))\n",
    "\n",
    "print('ZX = ' + str(average_data(result.get_counts(bellZX),observable_correlated)))\n",
    "print('XZ = ' + str(average_data(result.get_counts(bellXZ),observable_correlated)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see that for the state $|\\psi\\rangle= (|00\\rangle+|11\\rangle)/\\sqrt{2}$, expectation values (within experimental errors) are\n",
    "\n",
    "\n",
    "Observable    | Expected value |Observable    | Expected value|Observable    | Expected value\n",
    "------------- | -------------  | ------------- | ------------- | ------------- | -------------\n",
    "ZZ  | 1   |XX  | 1  | ZX  | 0 \n",
    "ZI  | 0   |XI  | 0  | XZ  | 0\n",
    "IZ  | 0   |IX  | 0  |   |\n",
    "\n",
    "How do we explain this situation? Here we introduce the concept of a *hidden variable model*. If we assume there is a hidden variable $\\lambda$ and follow these two assumptions: \n",
    "\n",
    "* _Locality_: No information can travel faster than the speed of light. There is a hidden variable $\\lambda$ that defines all the correlations so that  $$\\langle A\\otimes B\\rangle = \\sum_\\lambda P(\\lambda) A(\\lambda) B(\\lambda).$$ \n",
    "                      \n",
    "* _Realism_: All observables have a definite value independent of the measurement ($A(\\lambda)=\\pm1$ etc.).\n",
    "\n",
    "then can we describe these observations? --- The answer is yes! \n",
    "\n",
    "Assume $\\lambda$ has two bits, each occurring randomly with probability 1/4. The following predefined table would then explain all the above observables:\n",
    "\n",
    "$\\lambda$    | Z (qubit 1) |Z (qubit 2)    | X (qubit 1)| X (qubit 2)   \n",
    "------------- | -------------  | ------------- | ------------- | ------------- \n",
    "00  | 1 | 1 | 1 | 1  \n",
    "01  | 1 | 1 |-1 |-1  \n",
    "10  |-1 |-1 |-1 |-1    \n",
    "11  |-1 |-1 | 1 | 1  \n",
    "\n",
    "Thus, with a purely classical hidden variable model, we are able to reconcile the measured observations we had for this particular Bell state. However, there are some states for which this model will not hold. This was first observed by John Stewart Bell in 1964.  He proposed a theorem that suggests that there are no hidden variables in quantum mechanics. At the core of Bell's theorem is the famous Bell inequality. Here we'll use a refined version of this inequality (known as the CHSH inequality, derived by John Clauser, Michael Horne, Abner Shimony, and Richard Holt in 1969) to demonstrate Bell's proposal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CHSH Inequality <a id='section2'></a>\n",
    "\n",
    "\n",
    "In the CHSH inequality, we measure the correlator of four observables: $A$ and $A'$ on $q_0$, and $B$ and $B'$ on $q_1$, which have eigenvalues $\\pm 1$. The CHSH inequality says that no local hidden variable theory can have  \n",
    "\n",
    "$$|C|>2$$ \n",
    "\n",
    "where \n",
    "\n",
    "$$C = \\langle B\\otimes A\\rangle + \\langle B\\otimes A'\\rangle+\\langle B'\\otimes A'\\rangle-\\langle B'\\otimes A\\rangle.$$\n",
    "\n",
    "What would this look like with some hidden variable model under the locality and realism assumptions from above? $C$ then becomes \n",
    "\n",
    "$$C = \\sum_\\lambda P(\\lambda) \\{ B(\\lambda) [ A(\\lambda)+A'(\\lambda)] + B'(\\lambda) [ A'(\\lambda)-A(\\lambda)]$$\n",
    "                      \n",
    "and $[A(\\lambda)+A'(\\lambda)]=2$ (or 0) while $[A'(\\lambda)-A(\\lambda)]=0$ (or 2) respectively. That is, $|C|=2$, and noise will only make this smaller. \n",
    " \n",
    "If we measure a number greater than 2, the above assumptions cannot be valid. (This is a perfect example of one of those astonishing counterintuitive ideas one must accept in the quantum world.) For simplicity, we choose these observables to be \n",
    "\n",
    " $$C = \\langle Z\\otimes Z\\rangle + \\langle Z\\otimes X\\rangle+\\langle X\\otimes X\\rangle-\\langle X\\otimes Z\\rangle.$$\n",
    "\n",
    "$Z$ is measured in the computational basis, and $X$ in the superposition basis ($H$ is applied before measurement). The input state $$|\\psi(\\theta)\\rangle = I\\otimes Y(\\theta)\\frac{|00\\rangle + |11\\rangle}{\\sqrt(2)} = \\frac{\\cos(\\theta/2)|00\\rangle + \\cos(\\theta/2)|11\\rangle+\\sin(\\theta/2)|01\\rangle-\\sin(\\theta/2)|10\\rangle}{\\sqrt{2}}$$ is swept vs. $\\theta$ (think of this as allowing us to prepare a set of states varying in the angle $\\theta$).\n",
    " \n",
    "Note that the following demonstration of CHSH is not loophole-free. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:18:47.024173Z",
     "start_time": "2018-09-29T01:18:47.020582Z"
    }
   },
   "outputs": [],
   "source": [
    "CHSH = lambda x : x[0]+x[1]+x[2]-x[3]\n",
    "measure = [measureZZ, measureZX, measureXX, measureXZ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:18:47.572898Z",
     "start_time": "2018-09-29T01:18:47.479209Z"
    }
   },
   "outputs": [],
   "source": [
    "# Theory\n",
    "sim_chsh_circuits = []\n",
    "sim_x = []\n",
    "\n",
    "sim_steps = 30\n",
    "for step in range(sim_steps):\n",
    "    theta = 2.0*np.pi*step/30\n",
    "    bell_middle = QuantumCircuit(q,c)\n",
    "    bell_middle.ry(theta,q[0])\n",
    "    for m in measure:\n",
    "        sim_chsh_circuits.append(bell+bell_middle+m)\n",
    "    sim_x.append(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:18:52.340060Z",
     "start_time": "2018-09-29T01:18:49.892654Z"
    }
   },
   "outputs": [],
   "source": [
    "job = execute(sim_chsh_circuits, backend=sim_backend, shots=sim_shots)\n",
    "result = job.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:18:52.353221Z",
     "start_time": "2018-09-29T01:18:52.345583Z"
    }
   },
   "outputs": [],
   "source": [
    "sim_chsh = []\n",
    "circ = 0\n",
    "\n",
    "for x in range(len(sim_x)):\n",
    "    temp_chsh = []\n",
    "    for m in range(len(measure)):\n",
    "        temp_chsh.append(average_data(result.get_counts(sim_chsh_circuits[circ].name),observable_correlated))\n",
    "        circ += 1\n",
    "    sim_chsh.append(CHSH(temp_chsh))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:18:52.907673Z",
     "start_time": "2018-09-29T01:18:52.896342Z"
    }
   },
   "outputs": [],
   "source": [
    "# Experiment\n",
    "real_chsh_circuits = []\n",
    "real_x = []\n",
    "\n",
    "real_steps = 10\n",
    "for step in range(real_steps):\n",
    "    theta = 2.0*np.pi*step/10\n",
    "    bell_middle = QuantumCircuit(q,c)\n",
    "    bell_middle.ry(theta,q[0])\n",
    "    for m in measure:\n",
    "        real_chsh_circuits.append(bell+bell_middle+m)\n",
    "    real_x.append(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:18:58.945910Z",
     "start_time": "2018-09-29T01:18:57.340419Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Job Status: job has successfully run\n"
     ]
    }
   ],
   "source": [
    "job = execute(real_chsh_circuits, backend=device_backend, shots=device_shots)\n",
    "job_monitor(job)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:20:24.189882Z",
     "start_time": "2018-09-29T01:20:23.376662Z"
    }
   },
   "outputs": [],
   "source": [
    "result = job.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:20:24.196213Z",
     "start_time": "2018-09-29T01:20:24.192401Z"
    }
   },
   "outputs": [],
   "source": [
    "real_chsh = []\n",
    "circ = 0\n",
    "\n",
    "for x in range(len(real_x)):\n",
    "    temp_chsh = []\n",
    "    for m in range(len(measure)):\n",
    "        temp_chsh.append(average_data(result.get_counts(real_chsh_circuits[circ].name),observable_correlated))\n",
    "        circ += 1\n",
    "    real_chsh.append(CHSH(temp_chsh))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:20:24.649661Z",
     "start_time": "2018-09-29T01:20:24.198270Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sim_x, sim_chsh, 'r-', real_x, real_chsh, 'bo')\n",
    "plt.plot([0, 2*np.pi], [2, 2], 'b-')\n",
    "plt.plot([0, 2*np.pi], [-2, -2], 'b-')\n",
    "plt.grid()\n",
    "plt.ylabel('CHSH', fontsize=20)\n",
    "plt.xlabel(r'$Y(\\theta)$', fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting graph created by running the previous cell compares the simulated data (sinusoidal line) and the data from the real experiment. The graph also gives lines at $\\pm 2$ for reference. Did you violate the hidden variable model?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the saved CHSH data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:20:27.212607Z",
     "start_time": "2018-09-29T01:20:27.205422Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.83203125, 1.208984375, 1.103515625, 0.744140625, -0.169921875, -0.78515625, -1.142578125, -1.11328125, -0.5390625, 0.111328125]\n"
     ]
    }
   ],
   "source": [
    "print(real_chsh)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Despite the presence of loopholes in our demonstration, we can see that this experiment is compatible with quantum mechanics as a theory with no local hidden variables. See the original experimental demonstrations of this test with superconducting qubits [here](https://arstechnica.com/science/2017/05/quantum-volume-one-number-to-benchmark-a-quantum-computer/) and [here](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.81.062325)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Two-, Three-, and Four-Qubit GHZ States<a id='section3'></a>\n",
    "\n",
    "What does entanglement look like beyond two qubits? An important set of maximally entangled states are known as GHZ states (named after Greenberger, Horne, and Zeilinger). These are the states of the form \n",
    "\n",
    "$|\\psi\\rangle = \\left (|0...0\\rangle+|1...1\\rangle\\right)/\\sqrt{2}$. The Bell state previously described is merely a two-qubit version of a GHZ state. The next cells prepare GHZ states of two, three, and four qubits. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:20:32.237346Z",
     "start_time": "2018-09-29T01:20:32.231344Z"
    }
   },
   "outputs": [],
   "source": [
    "# 2 - qubits \n",
    "\n",
    "# quantum circuit to make GHZ state\n",
    "q2 = QuantumRegister(2)\n",
    "c2 = ClassicalRegister(2)\n",
    "ghz = QuantumCircuit(q2, c2)\n",
    "ghz.h(q2[0])\n",
    "ghz.cx(q2[0],q2[1])\n",
    "\n",
    "# quantum circuit to measure q in standard basis \n",
    "measureZZ = QuantumCircuit(q2, c2)\n",
    "measureZZ.measure(q2[0], c2[0])\n",
    "measureZZ.measure(q2[1], c2[1])\n",
    "ghzZZ = ghz+measureZZ\n",
    "\n",
    "measureXX = QuantumCircuit(q2, c2)\n",
    "measureXX.h(q2[0])\n",
    "measureXX.h(q2[1])\n",
    "measureXX.measure(q2[0], c2[0])\n",
    "measureXX.measure(q2[1], c2[1])\n",
    "ghzXX = ghz+measureXX\n",
    "\n",
    "circuits2 = [ghzZZ, ghzXX]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:20:33.669595Z",
     "start_time": "2018-09-29T01:20:32.656648Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 541.8x258.86 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ghzZZ.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:20:34.852279Z",
     "start_time": "2018-09-29T01:20:33.672489Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 602x258.86 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ghzXX.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:20:35.697672Z",
     "start_time": "2018-09-29T01:20:34.855471Z"
    }
   },
   "outputs": [],
   "source": [
    "job2 = execute(circuits2, backend=sim_backend, shots=sim_shots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:23:19.582949Z",
     "start_time": "2018-09-29T01:23:18.853736Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result2 = job2.result()\n",
    "plot_histogram(result2.get_counts(ghzZZ))\n",
    "plot_histogram(result2.get_counts(ghzXX))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:23:22.155614Z",
     "start_time": "2018-09-29T01:23:22.147494Z"
    }
   },
   "outputs": [],
   "source": [
    "# 3 - qubits \n",
    "\n",
    "# quantum circuit to make GHZ state \n",
    "q3 = QuantumRegister(3)\n",
    "c3 = ClassicalRegister(3)\n",
    "ghz3 = QuantumCircuit(q3, c3)\n",
    "ghz3.h(q3[0])\n",
    "ghz3.cx(q3[0],q3[1])\n",
    "ghz3.cx(q3[1],q3[2])\n",
    "\n",
    "# quantum circuit to measure q in standard basis \n",
    "measureZZZ = QuantumCircuit(q3, c3)\n",
    "measureZZZ.measure(q3[0], c3[0])\n",
    "measureZZZ.measure(q3[1], c3[1])\n",
    "measureZZZ.measure(q3[2], c3[2])\n",
    "ghzZZZ = ghz3+measureZZZ\n",
    "\n",
    "measureXXX = QuantumCircuit(q3, c3)\n",
    "measureXXX.h(q3[0])\n",
    "measureXXX.h(q3[1])\n",
    "measureXXX.h(q3[2])\n",
    "measureXXX.measure(q3[0], c3[0])\n",
    "measureXXX.measure(q3[1], c3[1])\n",
    "measureXXX.measure(q3[2], c3[2])\n",
    "ghzXXX = ghz3+measureXXX\n",
    "\n",
    "circuits3 = [ghzZZZ, ghzXXX]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:23:24.852781Z",
     "start_time": "2018-09-29T01:23:23.616353Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 722.4x379.26 with 1 Axes>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ghzZZZ.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:23:26.064859Z",
     "start_time": "2018-09-29T01:23:24.859786Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 782.6x379.26 with 1 Axes>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ghzXXX.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:23:27.190750Z",
     "start_time": "2018-09-29T01:23:26.067445Z"
    }
   },
   "outputs": [],
   "source": [
    "job3 = execute(circuits3, backend=sim_backend, shots=sim_shots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:26:10.085360Z",
     "start_time": "2018-09-29T01:26:09.105112Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result3 = job3.result()\n",
    "\n",
    "plot_histogram(result3.get_counts(ghzZZZ))\n",
    "plot_histogram(result3.get_counts(ghzXXX))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:26:11.959943Z",
     "start_time": "2018-09-29T01:26:11.947964Z"
    }
   },
   "outputs": [],
   "source": [
    "# 4 - qubits \n",
    "\n",
    "# quantum circuit to make GHZ state \n",
    "q4 = QuantumRegister(4)\n",
    "c4 = ClassicalRegister(4)\n",
    "ghz4 = QuantumCircuit(q4, c4)\n",
    "ghz4.h(q4[0])\n",
    "ghz4.cx(q4[0],q4[1])\n",
    "ghz4.cx(q4[1],q4[2])\n",
    "ghz4.h(q4[3])\n",
    "ghz4.h(q4[2])\n",
    "ghz4.cx(q4[3],q4[2])\n",
    "ghz4.h(q4[3])\n",
    "ghz4.h(q4[2])\n",
    "\n",
    "# quantum circuit to measure q in standard basis \n",
    "measureZZZZ = QuantumCircuit(q4, c4)\n",
    "measureZZZZ.measure(q4[0], c4[0])\n",
    "measureZZZZ.measure(q4[1], c4[1])\n",
    "measureZZZZ.measure(q4[2], c4[2])\n",
    "measureZZZZ.measure(q4[3], c4[3])\n",
    "ghzZZZZ = ghz4+measureZZZZ\n",
    "\n",
    "measureXXXX = QuantumCircuit(q4, c4)\n",
    "measureXXXX.h(q4[0])\n",
    "measureXXXX.h(q4[1])\n",
    "measureXXXX.h(q4[2])\n",
    "measureXXXX.h(q4[3])\n",
    "measureXXXX.measure(q4[0], c4[0])\n",
    "measureXXXX.measure(q4[1], c4[1])\n",
    "measureXXXX.measure(q4[2], c4[2])\n",
    "measureXXXX.measure(q4[3], c4[3])\n",
    "ghzXXXX = ghz4+measureXXXX\n",
    "\n",
    "circuits4 = [ghzZZZZ, ghzXXXX]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:26:13.730966Z",
     "start_time": "2018-09-29T01:26:12.154391Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1023.4x499.66 with 1 Axes>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ghzZZZZ.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:26:15.292069Z",
     "start_time": "2018-09-29T01:26:13.733594Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1083.6x499.66 with 1 Axes>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ghzXXXX.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:26:16.316555Z",
     "start_time": "2018-09-29T01:26:15.294849Z"
    }
   },
   "outputs": [],
   "source": [
    "job4 = execute(circuits4, backend=sim_backend, shots=sim_shots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-29T01:30:17.934041Z",
     "start_time": "2018-09-29T01:26:16.318708Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result4 = job4.result()\n",
    "\n",
    "plot_histogram(result4.get_counts(ghzZZZZ))\n",
    "plot_histogram(result4.get_counts(ghzXXXX))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mermin's Test and the Three Box Game<a id='section4'></a>\n",
    "In case the violation of Bell's inequality (CHSH) by two qubits is not enough to convince you to believe in quantum mechanics, we can generalize to a more stringent set of tests with three qubits, which can give a single-shot violation (rather than taking averaged statistics). A well-known three-qubit case is Mermin's inequality, which is a test we can perform on GHZ states. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An example of a three-qubit GHZ state is $|\\psi\\rangle = \\left (|000\\rangle+|111\\rangle\\right)/\\sqrt{2}$. You can see this is a further generalization of a Bell state and, if measured, should give $|000\\rangle$ half the time and $|111 \\rangle$ the other half of the time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:02:55.697908Z",
     "start_time": "2018-09-26T15:02:55.690169Z"
    }
   },
   "outputs": [],
   "source": [
    "# quantum circuit to make GHZ state \n",
    "q3 = QuantumRegister(3)\n",
    "c3 = ClassicalRegister(3)\n",
    "ghz3 = QuantumCircuit(q3, c3)\n",
    "ghz3.h(q3[0])\n",
    "ghz3.cx(q3[0],q3[1])\n",
    "ghz3.cx(q3[0],q3[2])\n",
    "\n",
    "# quantum circuit to measure q in standard basis \n",
    "measureZZZ = QuantumCircuit(q3, c3)\n",
    "measureZZZ.measure(q3[0], c3[0])\n",
    "measureZZZ.measure(q3[1], c3[1])\n",
    "measureZZZ.measure(q3[2], c3[2])\n",
    "ghzZZZ = ghz3+measureZZZ\n",
    "\n",
    "circuits5 = [ghzZZZ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:02:57.387523Z",
     "start_time": "2018-09-26T15:02:56.036994Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 722.4x379.26 with 1 Axes>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ghzZZZ.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:04:06.589602Z",
     "start_time": "2018-09-26T15:04:06.477829Z"
    }
   },
   "outputs": [],
   "source": [
    "job5 = execute(circuits5, backend=sim_backend, shots=sim_shots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:04:04.552475Z",
     "start_time": "2018-09-26T15:04:04.080521Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result5 = job5.result()\n",
    "\n",
    "plot_histogram(result5.get_counts(ghzZZZ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose we have three independent systems, $\\{A, B, C\\}$, for which we can query two particular questions (observables) $X$ and $Y$. In each case, either query can give $+1$ or $-1$. Consider whether it is possible to choose some state of the three boxes, such that we can satisfy the following four conditions: $X_A Y_B Y_C = 1$, $Y_A X_B Y_C =1$, $Y_A Y_B X_C = 1$, and $X_A X_B X_C = -1$. Classically, this can be shown to be impossible... but a three-qubit GHZ state can in fact satisfy all four conditions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:04:13.252830Z",
     "start_time": "2018-09-26T15:04:13.249189Z"
    }
   },
   "outputs": [],
   "source": [
    "MerminM = lambda x : x[0]*x[1]*x[2]*x[3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:04:13.721485Z",
     "start_time": "2018-09-26T15:04:13.714469Z"
    }
   },
   "outputs": [],
   "source": [
    "observable ={'000': 1, '001': -1, '010': -1, '011': 1, '100': -1, '101': 1, '110': 1, '111': -1}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:04:15.802293Z",
     "start_time": "2018-09-26T15:04:15.786130Z"
    }
   },
   "outputs": [],
   "source": [
    "# quantum circuit to measure q XXX \n",
    "measureXXX = QuantumCircuit(q3, c3)\n",
    "measureXXX.h(q3[0])\n",
    "measureXXX.h(q3[1])\n",
    "measureXXX.h(q3[2])\n",
    "measureXXX.measure(q3[0], c3[0])\n",
    "measureXXX.measure(q3[1], c3[1])\n",
    "measureXXX.measure(q3[2], c3[2])\n",
    "ghzXXX = ghz3+measureXXX\n",
    "\n",
    "# quantum circuit to measure q XYY\n",
    "measureXYY = QuantumCircuit(q3, c3)\n",
    "measureXYY.s(q3[1]).inverse()\n",
    "measureXYY.s(q3[2]).inverse()\n",
    "measureXYY.h(q3[0])\n",
    "measureXYY.h(q3[1])\n",
    "measureXYY.h(q3[2])\n",
    "measureXYY.measure(q3[0], c3[0])\n",
    "measureXYY.measure(q3[1], c3[1])\n",
    "measureXYY.measure(q3[2], c3[2])\n",
    "ghzXYY = ghz3+measureXYY\n",
    "\n",
    "# quantum circuit to measure q YXY\n",
    "measureYXY = QuantumCircuit(q3, c3)\n",
    "measureYXY.s(q3[0]).inverse()\n",
    "measureYXY.s(q3[2]).inverse()\n",
    "measureYXY.h(q3[0])\n",
    "measureYXY.h(q3[1])\n",
    "measureYXY.h(q3[2])\n",
    "measureYXY.measure(q3[0], c3[0])\n",
    "measureYXY.measure(q3[1], c3[1])\n",
    "measureYXY.measure(q3[2], c3[2])\n",
    "ghzYXY = ghz3+measureYXY\n",
    "\n",
    "# quantum circuit to measure q YYX\n",
    "measureYYX = QuantumCircuit(q3, c3)\n",
    "measureYYX.s(q3[0]).inverse()\n",
    "measureYYX.s(q3[1]).inverse()\n",
    "measureYYX.h(q3[0])\n",
    "measureYYX.h(q3[1])\n",
    "measureYYX.h(q3[2])\n",
    "measureYYX.measure(q3[0], c3[0])\n",
    "measureYYX.measure(q3[1], c3[1])\n",
    "measureYYX.measure(q3[2], c3[2])\n",
    "ghzYYX = ghz3+measureYYX\n",
    "\n",
    "circuits6 = [ghzXXX, ghzYYX, ghzYXY, ghzXYY]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:04:18.737346Z",
     "start_time": "2018-09-26T15:04:17.502295Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 842.8x379.26 with 1 Axes>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ghzXXX.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:04:20.144740Z",
     "start_time": "2018-09-26T15:04:18.739473Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 903x379.26 with 1 Axes>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ghzYYX.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:04:21.654700Z",
     "start_time": "2018-09-26T15:04:20.146870Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 903x379.26 with 1 Axes>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ghzYXY.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:04:23.171284Z",
     "start_time": "2018-09-26T15:04:21.667294Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 903x379.26 with 1 Axes>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ghzXYY.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:04:51.953667Z",
     "start_time": "2018-09-26T15:04:51.624434Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Job Status: job has successfully run\n"
     ]
    }
   ],
   "source": [
    "job6 = execute(circuits6, backend=device_backend, shots=device_shots)\n",
    "job_monitor(job6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:06:31.992339Z",
     "start_time": "2018-09-26T15:06:31.608356Z"
    }
   },
   "outputs": [],
   "source": [
    "result6 = job6.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-26T15:06:32.218278Z",
     "start_time": "2018-09-26T15:06:32.211723Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.01893309672595933\n"
     ]
    }
   ],
   "source": [
    "temp=[]\n",
    "temp.append(average_data(result6.get_counts(ghzXXX),observable))\n",
    "temp.append(average_data(result6.get_counts(ghzYYX),observable))\n",
    "temp.append(average_data(result6.get_counts(ghzYXY),observable))\n",
    "temp.append(average_data(result6.get_counts(ghzXYY),observable))\n",
    "print(MerminM(temp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above shows that the average statistics are not consistent with a local hidden variable theory. To demonstrate with single shots, we can run 50 single experiments, with each experiment chosen randomly, and the outcomes saved. If there was a local hidden variable theory, all the outcomes would be $+1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}