GHZ-Game.ipynb

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   },
   "source": [
    "# The GHZ-Game\n",
    "\n",
    "\n",
    "### Solve \"unsolvable\" problems using Quantum Computers\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "## Usage instructions for the user interface\n",
    "\n",
    "* \"Shift Enter\" executes the interactive cells (might need to click the cell, first)\n",
    "* Execute all the interactive cells (\"In [1]:\", etc)"
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "First we need to install some prerequisits. You do not have to understand them for now (just click on the cells and press \"Shift Enter\"):"
   ]
  },
  {
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   },
   "outputs": [],
   "source": [
    "#import prerequisites\n",
    "from ipywidgets import interact\n",
    "from qiskit.quantum_info import Statevector\n",
    "from qiskit.tools.visualization import plot_histogram, plot_bloch_multivector, plot_bloch_vector, plot_state_qsphere\n",
    "from GHZGame.ghzGame import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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     "name": "#%%\n"
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    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# create the quantum circuit with the chosen coin moves\n",
    "q = QuantumRegister(3) # create a quantum register with one qubit\n",
    "# create a classical register that will hold the results of the measurement\n",
    "c = ClassicalRegister(3) \n",
    "qc = QuantumCircuit(q, c) # creates the quantum circuit\n",
    "backend = BasicAer.get_backend('qasm_simulator') # define the backend, here a Quantum simulator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
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     "slide_type": "slide"
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   },
   "source": [
    "# Let's play a game!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
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    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We form two teams of three players. Your team is called \"Team Einstein\" and your team members are Alice and Bob (and you, of course). The other team is called \"Team Schrödinger\" and - as the name indicates - will be able to exploit quantum mechanics."
   ]
  },
  {
   "cell_type": "markdown",
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     "name": "#%% md\n"
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    "slideshow": {
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   },
   "source": [
    "## The rules for this game are as follows:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "name": "#%% md\n"
    }
   },
   "source": [
    "- Each player thinks of a color (red or blue) and a shape (star or rectangle)."
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "- The game master than asks either all players for a color or one for a color and two for a shape. In total, four different kinds of questions can be asked:\n",
    "\n",
    "\n",
    "1. Color, color, color\n",
    "2. Color, shape, shape\n",
    "3. Shape, color, shape\n",
    "4. Shape, shape, color\n",
    "\n",
    "Which of the four sets of questions is used, is chosen randomly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Once the questions are asked, the team members are not allowed to communicate anymore. Before that, the team members are allowed to agree on a strategy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "- In the case that all players are asked for a color (1.), the team wins if an even number of people answered with red. Otherwise (when two are asked for a shape and only one for a color) they win if an uneven number of players answered with either red or star depending on the question they were asked. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "### Example:\n",
    "\n",
    "Question: Color, color, color\n",
    "\n",
    "Answer: red, red, blue\n",
    "> right answer, even number of red.\n",
    "\n",
    "Question: Color, shape, shape\n",
    "\n",
    "Answer: red, star, rectangle\n",
    "> wrong answer, even number of red and star, should be uneven.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": ""
    }
   },
   "source": [
    "If you think about a *real* object that will answer the question about color and shape, each team member could  choose to think of one of the following four objects.  You are allowed to change your mind as often as you want as long as you do not know whether your team members were asked for a color or a shape:\n",
    "![title](GHZGame/shapes.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Make your choices:\n",
    "(The 0 or 1 inside the brakets of the drop down fields below show the corresponding bit value. 0 is interpreted as red or star and 1 as blue or rectangle.)"
   ]
  },
  {
   "cell_type": "code",
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     "is_executing": true,
     "name": "#%%\n"
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    "scrolled": false,
    "slideshow": {
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    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your team can now discuss which values each of you will say when asked either for the color or the shape of your object.\n",
      "\n",
      "Alice:\n"
     ]
    },
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      "text/plain": [
       "interactive(children=(Dropdown(description='AlicesColor', options={'red (1)': 1, 'blue (0)': -1}, value=1), Dr…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bob:\n"
     ]
    },
    {
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      "text/plain": [
       "interactive(children=(Dropdown(description='BobsColor', options={'red (1)': 1, 'blue (0)': -1}, value=1), Drop…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "You:\n"
     ]
    },
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      "text/plain": [
       "interactive(children=(Dropdown(description='YourColor', options={'red (1)': 1, 'blue (0)': -1}, value=1), Drop…"
      ]
     },
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     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "print ('Your team can now discuss which values each of you will say when asked either for the color or the shape of your object.')\n",
    "print ('')\n",
    "\n",
    "print ('Alice:')\n",
    "interact(Alice, AlicesColor={'red (1)':1,'blue (0)':-1}, AlicesShape={'star (1)':1,'rectangle (0)':-1})\n",
    "\n",
    "print ('Bob:')\n",
    "interact(Bob, BobsColor={'red (1)':1,'blue (0)':-1}, BobsShape={'star (1)':1,'rectangle (0)':-1})\n",
    "\n",
    "print ('You:')\n",
    "interact(You, YourColor={'red (1)':1,'blue (0)':-1}, YourShape={'star (1)':1,'rectangle (0)':-1})\n",
    "print ('')"
   ]
  },
  {
   "cell_type": "markdown",
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     "name": "#%% md\n"
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    }
   },
   "source": [
    "If you are confident with your choices try it out here. Do you have a 100% winning strategie that gives the correct answer for each of the four sets of questions? (\"If you loose once, you will stay in prison forever\".)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
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     "name": "#%%\n"
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    "slideshow": {
     "slide_type": "fragment"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Round  1 , Question  1\n",
      "Team Einstein was wrong, Team Schrödinger was right\n",
      "Round  2 , Question  2\n",
      "Both teams were right\n",
      "Round  3 , Question  3\n",
      "Both teams were right\n",
      "Round  4 , Question  4\n",
      "Both teams were right\n"
     ]
    }
   ],
   "source": [
    "# runs the experiment for both teams, asking all four questions.\n",
    "runExperiment()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Why has the other team a 100% winning strategie while your team does not?\n",
    "\n",
    "To find out what they do differently you talk to team Schrödinger and their team member Erwin explains what they did."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Bob: \n",
    "\"*How did you do that? Isn't it impossible to constantly win this game? I mean look at this, we tried to solve it mathematically and the problem is unsolvable, you must have cheated!*\"\n",
    "\n",
    "(For easier calculations we replaced 0 for blue and rectangle with -1)\n",
    "    \n",
    "\n",
    "    \n",
    "   ![title](GHZGame/proof1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Erwin (from team Schrödinger): \n",
    "\"*Yes, you are right, but we did not cheat! We used so-called qubits and entanglement and with that it is possible to always win.*\"\n",
    "\n",
    "Bob: \n",
    "\"*What exactly is that and how does it work?*\"\n",
    "    \n",
    "Erwin: \n",
    "\"*Each of us had a qubit. You can imagine them as a little sphere with a vector pointing in \n",
    "    one direction. This vector describes the state the qubit is currently in.*\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_bloch_vector([1,0,0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Erwin: \n",
    "\"*However - as you know from quantum mechanics - you cannot see in which state the qubit is, but \n",
    "    need to measure it to find out something about its state. The result of a measurement is always \n",
    "    either 0 or 1. These values correspond to the shape and color of the objects in such a way that we \n",
    "    answered with red or star whenever measuring 1 and accordingly with blue or rectangle when measuring 0.\n",
    "    For example, when asked for the color of your object and you are measuring a 0 you answer blue. For a 1 \n",
    "    your answer would be red.*\n",
    "    \n",
    "*The vector in the sphere above, is in a position other than 0 (top of the sphere) or 1 (at the bottom). When \n",
    "    measuring, you would still get one of these results. In this case, it would be 0 with 50% probability \n",
    "    and 1 with 50% probability. The actual result for a single measurement is random.*\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Erwin: \n",
    "\"*So we used qubits that were entangled with each other and different \"observables\" of a quantum object. Normally, a Quantum Computer measures the Z-basis of a qubit but we measured X when asked for a color and when asked for a shape we measured Y. The result for the Y measurement in the example above \n",
    "    would always be 1, instead of the 50% probability of 0 or 1 when measuring the Z-value. \n",
    "    I will explain later why exactly this works but as all three of our qubits were entangled, we got the correct answer for all cases.*\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Bob: \n",
    "\"*But isn't that against the rule to not communicate with each other after the question was asked?*\"\n",
    "    \n",
    "Erwin: \n",
    "\"*No it is not because the qubits do not communicate with each other. They are just correlated in \n",
    "    such a way that they cannot be seen as independent. We can just try it out :) Before we start we \n",
    "    need to bring all our three qubits into the so-called GHZ-state. This is an entangled state that creates \n",
    "    dependencies between the qubits. To do so, we need to apply the following Quantum circuit:*\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lugb4zS448aW5+61vhA174Ogpc/cr1uvfvz833XQT/fv3t7oU0ygA2pGenk5KSgoRERGEhYUxYcIE1q5dS11dndWlyRUyDPjdPsg90zn7bzLgjU7cv1jj3LlzvPnmm5w7d87qUkyjAGjDM888Q3JyMu+//z4ul4urr76arKwsVq5cSVJSEtXV1VaXKFfgky/grwW+bfOLFHj8Zs9vbzQ2wX9//PXwUen5ioqKWLNmDUVFRVaXYhoFwDccPHiQFStW4HA42LBhA/n5+WRkZJCVlcWYMWPYv38/jz76qNVlSgeVVHoe2Pqqbyj0D/P89tbfKzwPl0W6KwXAN6xevRrDMLjnnntYtGhRy+sxMTGsX78egJdeeokzZ3R/3xOl/9Uzwaur7P0bFJd33fFEfOH3AVBcXExqaipjxozB6XQyfPhwli9fTmVlJUuWLMHhcPDCCy8AUF5eTnp6OgBLly69aF9z5swhLi6Ouro6tmzZ0qXnIVeuqg4+7eJZ/Aaw33++QEr8jF8HwNGjR5kwYQJPPfUUbrebcePGUV9fz/PPP88dd9zRsrLfNddcA0BGRgZ1dXWEhIQwZcqUNvc5e/ZsAA4cONAl5yDmOfQF1Jkw3NNXn+SaM8xUrNW7d29mzZpF7969rS7FNH4bAMXFxSxYsAC3281DDz1EUVERR44cwe12k5aWxrZt2zh06BAOh4PExEQAsrOzARg5ciSBgW3PkYuJiWnVVnqOzEJrjltZCyeLrTm2mCc6OppXX32V6Ohoq0sxjd8GwLJlyygoKOCBBx7g6aefxuVytbyXmprKxIkTaWhoIDo6mr59PVM3S0pKABgwYEC7+21+r7mt9AyGAactHL1n5bHFHI2NjVRUVNDY6D+3c34ZACdOnGDjxo1ERkaydu3aNttMnjwZgIkTJ7a8VlNTA0BwcHC7+w4JCQFoNRS0OWimTZtGSEgIDoeWiexuSio9zwCsUqAA6PGysrKYOnUqWVlZVpdiGr8MgLfeeoumpibuuusu+vTp02ab0FDPeL4LA8DpdAJccrJXbW1tq+0BcnJy2Lx5M0OGDGHq1KlXXL+Yr8TiFXxLKq09vkhb/HIxuJ07dwKQlJTUbpuCAs9MoAsDwJvunba6iebMmdMyOeTxxx9n3759Hay8tSlTpuB2u03Zl90NGjObOUt/3+Z7v0i5/Pj+vs6vfz9+c/vtzlfDszsufv3wkaNE3Xujl9V2P99beYiwfkMpchcRFeUfH3IWL17sU/vm/8e3b99ORkaGV9ts2LDBx6p8N2TIEA4fPtyhbf0yAE6ePAl4Hua2paGhoeUifWEAxMXFtWzf0NDQ5oPg3NzcVm0BAjppDWC3201hoUVPLv2Nq/3Zm82TvLwREOB92wvVVFf26P+Wzf3ejY2NPfo8LuTrF7s0dxHX1NR4vW13/7PyywCorPTcb7e3ZMPGjRspLi7G5XIxatSoltcnTZpEcHAwtbW1HD58mBkzZly07d69ewGYPn16J1Te2pAhQzr9GHbhCm0/pM97sbJHX6fn4t/UBOdr2m/X3r6M+vIevYpkr169Wn735PO4UFiYb0ne3EXsdDq93rYr/qyu5DrhlwEwZMgQSkpKOHLkCDNnzmz1XlFREStWrAAgMTGx1QNbl8vFvHnz2LZtG6+88spFAbB7926ys7MJDg5m4cKFnX4eHb2tk4s1NcEjf2h7HkBbXTbf9PjNnk/+52vg8Xd8P/4Pf5DCH5/0cQGibuSxtz3fezB0yNCW7tOezteHufX19SxZsgSXy0VQUJBX26xZs6YjpXUZv3wIfP311wOQlpbWarz+oUOHSEpKorjYMyi7eQLYhVatWoXD4eC1117j9ddfb3k9NzeXJUuWAHDfffcxaNCgTjwDMVtAAAxrf3Rvpxsebt2xxRxBQUGEh4d7ffHvCfwyAFJTU4mIiOD06dMkJCQwYcIEYmNjmTZtGqNHj2bu3LlA6/7/ZjNmzGDdunUYhsHixYuJjo5m0qRJjB07lpycHKZPn866deu6+pTEBGMGW3PcwAAYGWnNscU8p06d4v777+fUKf/5sge/DICoqCj27NnD/PnzcTqd5OfnEx4ezssvv8y2bdta7graCgDwBMiOHTuYN28eZWVlZGVlERcXxxNPPMFHH33kc9+hdA8zx4AVUzQmjYTeIV1/XDFXeXk5u3btorzcf1b388tnAADx8fFs3br1otcrKirIz88nICCA8ePHt7t9cnIyycnJnVmidLHwPpAwzPfvArhSs+Iu30bECn4bAO05fvw4hmEQFxdn6if5TZs2AZCZmdnq36Ojo9tdWE663g3j4XihZ2mIrjB2KIyM6JpjifjKdgHw2WefAe13/3TUbbfd1ua/L1q0qEsmg4h3RkTA3Hj4ILPzj+UMgjumW9PtJOINBYBJjK76SClXLCXRcxfgLvN+m+bx/d7MGWh282QY4D8rB9ve4MGDefjhhxk82KLRBJ1AASC2E9QL7kuC59Kh1MvJoN7MFbjQ9QkwPcb32qT7ioyM9Hn5iO7OL0cBXcrOnTsxDIP58+dbXYpYaEBv+Nk8iGh7rcArcsN4mK/PF36nrKyMHTt2UFbmw61jN2e7ABBpFtEHHkz2DNM0Q+8QWDQbvjdR/f7+qKCggAcffNBvZkKDDbuARC7Ux+m5aF8zAt4+7FnuwFcO4JqR8M9TwOU0vUSRTqMAEAEmjoDxUZ45Avs+h2wvVuEOC4YZMXBtLES6Lt9epLtRAIj8Q68ATxBMHAFVtVBQAqf+DsXl0NDoWU8oNNizptDwcBjc1/OaSE+lABBpQ1gIxA3x/IiAZxno+Pj4lmWh/YECQETECzExMbz99ttWl2Eq3cCKiNiUAkBExAuZmZkkJia2rPflDxQAIiJeMAyD+vp6v1r2RQEgImJTCgAREZtSAIiI2JSGgYqIeCEmJoYtW7YwfPhwq0sxjQJARMQLTqeT2NhYq8swlbqARES8UFhYyKpVqygsLLS6FNMoAEREvFBaWsrmzZspLS21uhTTKABERGxKASAiYlMKABERm1IAiIh4ITIykqVLlxIZGWl1KaZRAIiIeMHhcBAcHIzDj77wWQEgIuKFs2fP8uKLL3L27FmrSzGNAkBExKYUACIiNqUAEBGxKQWAiIgX+vXrx4IFC+jXr5/VpZhGi8GJiHghKiqKX/3qV1aXYSrdAYiIeKG2tpaTJ09SW1trdSmmUQCIiHghJyeHlJQUcnJyrC7FNAoAERGbUgCIiNiUAkBExKYUACIiNqVhoCIiXkhISODEiRNWl2Eq3QGIiNiUAkBELskwPD/N/2xXeXl53HnnneTl5VldimnUBSQirdQ2wF9OQV4xFJyDL0ugocnz3vkaeGILjIiA4eEwcQQM6G1tvV2lqqqKY8eOUVVVZXUpplEAiAgAZ8thz9/g4BdQU3/pdmfL4dN8+J8MGD8MvnU1xA3pslLFJAoAEZtrbIJdJ+C9v3j+2ReGAZ8VeH4mjYRbpkAfZ+fUKeZTAIjYWEklvLYHTv39yveVcRI+/wrumgnxV135/qTz6SGwiE2dPQ/PpZtz8W9WUQOvfOgJA38zbNgw0tLSGDZsmNWlmEYB0I709HRSUlKIiIggLCyMCRMmsHbtWurq6qwuTeSKlVbBix94fputyYA39sHxAvP3baX+/ftz00030b9/f6tLMY0CoA3PPPMMycnJvP/++7hcLq6++mqysrJYuXIlSUlJVFdXW12iSIc1GfBf+zvn4t/qGB9Dmf8MmOHcuXO8+eabnDt3zupSTKMA+IaDBw+yYsUKHA4HGzZsID8/n4yMDLKyshgzZgz79+/n0UcftbpMkQ7b/znkfOXbNr9Igcdv9vz2VnUd/OGg/8wdKCoqYs2aNRQVFVldimkUAN+wevVqDMPgnnvuYdGiRS2vx8TEsH79egBeeuklzpw5Y1WJIh1WXgNbMnzfrm8o9A/z/PbF8UL4y2nfjyddw+8DoLi4mNTUVMaMGYPT6WT48OEsX76cyspKlixZgsPh4IUXXgCgvLyc9PR0AJYuXXrRvubMmUNcXBx1dXVs2bKlS89DxAwHcqCuoWuP+VFW1x5PvOfXAXD06FEmTJjAU089hdvtZty4cdTX1/P8889zxx13tCzsdM011wCQkZFBXV0dISEhTJkypc19zp49G4ADBw50yTmImKWpydP909W+OOuZTSzdj98GQHFxMQsWLMDtdvPQQw9RVFTEkSNHcLvdpKWlsW3bNg4dOoTD4SAxMRGA7OxsAEaOHElgYNtTJGJiYlq1Fekpcs9AiUUPZQ/5wfI5vXv3ZtasWfTu7T9rX/htACxbtoyCggIeeOABnn76aVwuV8t7qampTJw4kYaGBqKjo+nbty8AJSWejykDBgxod7/N7zW3FekpTpo43t9XZs41sEp0dDSvvvoq0dHRVpdiGr8MgBMnTrBx40YiIyNZu3Ztm20mT54MwMSJE1teq6mpASA4OLjdfYeEhAC0Ggq6adMmbrnlFkaOHElYWBhjx47ll7/8JRUVFVd8LiJmOW3h6MWCc56hoT1ZY2MjFRUVNDY2Wl2KafwyAN566y2ampq466676NOnT5ttQkM9wxkuDACn07OIyaUme9XW1rbaHuDpp5+mV69ePPnkk7z33nv85Cc/4aWXXiIlJYWmJh8XVxHpJO5S645d29Dz5wRkZWUxdepUsrL856m2X64FtHPnTgCSkpLabVNQ4JmmeGEAeNO901Y30bvvvsvAgQNb/v26665j4MCB3HXXXezdu5c5c+Z04CxgypQpuN3uDm0r8k3ffeQAvQdEtfneL1IuPcSzr/Pr34/ffOnjnK+GZ3dc/Pq130qi/IwFT6HbsXjxYp/aN4//3759OxkZ3o2l3bBhg49V+W7IkCEcPny4Q9v6ZQCcPOlZiGTkyJFtvt/Q0MC+ffuA1gEQFxfXsn1DQ0ObD4Jzc3NbtQVaXfybNY8iKiws7MgpAOB2u69oe5ELNTa0P/6zeZz/5QQEeNeuLV995abky+7z99nXdf2bu4hramq83ra7///rlwFQWVkJ0O6SDRs3bqS4uBiXy8WoUaNaXp80aRLBwcHU1tZy+PBhZsyYcdG2e/fuBWD69OmXrGHXrl0AxMfHd+gcwJPsImYxmmrbfe/8ZVY36ev0XPybmjxfCnMp7e0rYoCLMEf3WUgtLMy3JGvuInY6nV5v2xULx13JdcJhGP4yUftr48aN48SJE7zwwgv89Kc/bfVeUVERkydPpqioiFmzZrVc0JvdeOONbNu2jXvvvbdl5m+z3bt3c9111xEcHMzp06cZNGhQm8cvLCxk0qRJTJ48mffee8/ckxPpoA174Oipjm37+M2eT/6lVfD4O75v7wyCJ2+DAEfHjt8ZfO3LP378OLfeeiubNm0iISHBq23Gjh3bkdK6jF8+BL7++usBSEtLazVe/9ChQyQlJVFcXAx8PQHsQqtWrcLhcPDaa6/x+uuvt7yem5vLkiVLALjvvvvavfhXVFSwcOFCgoOD+e1vf2vWKYlcsahwa4/dnS7+HREXF8e+fftadf/2dH4ZAKmpqURERHD69GkSEhKYMGECsbGxTJs2jdGjRzN37lygdf9/sxkzZrBu3ToMw2Dx4sVER0czadIkxo4dS05ODtOnT2fdunVtHre6upoFCxaQl5dHeno6Q4cO7dTzFPHFyEjrjj0iwrpjmyUoKIjw8HCCgoKsLsU0fhkAUVFR7Nmzh/nz5+N0OsnPzyc8PJyXX36Zbdu2tdwVtBUA4AmQHTt2MG/ePMrKysjKyiIuLo4nnniCjz76qM3+v/r6em699VYOHz7Me++9x7hx4zr1HEV8FTPQui9wnzrq8m26u1OnTnH//fdz6lQH+9G6Ib98CAyeh69bt2696PWKigry8/MJCAhg/Pjx7W6fnJxMcnKyV8dqnnPwwQcfsH37dqZNm9bhukU6S0AAzIqFrUe79rgxg2Bo/649ZmcoLy9n165dFz1X7Mn8NgDac/z4cQzDIC4uzudRAO356U9/yh//+EceeeQRwsLCWi0UFxMT0+YwURErzIiBP//VMzGrq1zXvZ+D2ppfdgFdymeffQa03/3TEc0jfdatW8fMmTNb/Wzbts2044hcqT5OuOmfuu5446NgQttzz6QbsN0dQGcEQH5+vmn7Euls146BY6cg24dJ5s1j+y83X+BCYcFw+zRw9PDRP/5MASBiMw4H3DUTnkuHc5XebdPW0g6XEuCAf5nl+zeIdWeDBw/m4YcfZvDgwVaXYhq/nAgmIpdXXA4vfgAlXoaAt3oFwN2zYOIIc/drtq5Y1E0TwUSkW4p0wfIbINrE+QF9nfCjb3f/i39HlJWVsWPHDsrKyqwuxTQKABEb6x8Gy+bBwn+CoF5Xtq8p0fDwjXC1n85/LCgo4MEHH2xZSdgf2O4ZgIi0FhAASfGQOBz2ZsMnuVDV/lditN7W4dnuW3EQ4z9d47ahABARACL6eO4EvpsIfy2A/GLPt4h9WfL1vIFeATDIBVERMCLcc/HvZ850GrGAAkBEWgkOhH+K9vw0azLAMDwBIP5DASAilxXgAGw+nt/pdBIfH9/yvQD+QMNARcSWNAxUo4BERGxLASAi4oXMzEwSExPJzMy0uhTTKABERLxgGAb19fX4U6+5AkBExKYUACIiNqUAEBGxKc0DEBHxQkxMDFu2bGH48OFWl2IaBYCIiBecTiexsbFWl2EqdQGJiHihsLCQVatWUVhYaHUpplEAiIh4obS0lM2bN1NaWmp1KaZRAIiI2JQCQETEphQAIiI2pdVARUS8UFRUxMsvv8x9993H0KH+8b2XCgAREZtSF5CIiE0pAEREbEoBICJiUwoAERGbUgCIiNiUAkBExKYUACIiNqUAEBGxKQWAiIhNKQBERGxKASAiYlMKgB7sjTfeYPLkyQwYMIDQ0FDi4+N59tln0fJOIuINfSdwDzZo0CD+7d/+jauvvpqQkBD27NnD/fffT69evVi+fLnV5YlIN6fVQP3MzTffDMA777xjcSUi0t2pC8hPGIbBwYMH2bdvH0lJSVaXIyI9gLqAeriysjKGDRtGXV0dTU1NPPbYYyxbtszqskSkB1AA9HAul4ujR49SVVXF/v37efTRR7nqqqtYsmSJ1aWJSDenZwB+Zu3atTz33HO43W6rSxGRbk7PAPxMU1MTNTU1VpchIj2AuoB6sMcee4xvfetbjB49mvr6enbv3k1aWhr33HOP1aWJSA+gO4ArcP78eR555BFiY2NxOp0MHjyYW265hcOHD3fZ8X/84x+TkJDAjBkz+PWvf83atWt59tlnu+T4ItKz6RlAB505c4Zrr72W3NxcnE4n48aN48svv8TtdhMYGMjvf/97brnlFqvLFBFpl+4AOujee+8lNzeX6dOnc/LkST799FMKCgpYvXo1DQ0N3H333RQWFlpdZov8Ajd19Q1WlyEi3YjuADrg008/ZcqUKQQGBpKdnc2oUaNavT937lx27drFz3/+c/793//doiq/VlldQ9qv3yI4MJCf/MtCIvr3tbokEekGdAdwgcbGRt544w1uuOEGBg4cSEhICCNGjCAlJYVXX32VxsZGADZv3gzAd77znYsu/gBLly4FYNOmTV1X/CXsPfQX6urqcfUJI7yfy+pyRKSbUAD8w/nz55k3bx533303f/7znwkODmbixIk0NTWRnp7O0qVLKS8vB+DAgQMAzJ49u819Nb9eUFBAQUFB15xAOyqra9j36XEArp81GYfDYWk9ItJ9aBjoPyxZsoRdu3YRFRXF7373u1br6Xz11VesX7+eoKAgALKzswGIiYlpc19RUVEEBwdTV1dHdnY2UVFRnX8C7Wj+9D90UATjYkdaVoeIdD96BkDrPv2MjAzGjx9/yfa9e/emqqqK9957j5SUlDbbDB48mDNnzrBp06YOjwb6z9ffpryiukPbAjQZBhWVVQCEOkMIClTei/gbV59Qfrbonzu0ra4IwJ/+9CcA5s+ff9mLP9Ay0zY4OLjdNiEhIQBUV3f8Al5eUc35isoOb3+h6ppaqqk1ZV8i4h8UAEBmZiYAM2fO9Kq90+mkqqqKurq6dtvU1noutqGhoR2uy9Wn49vq07+IPVzJdUJXBTwPgAH69evnVfsBAwZQVVVFSUlJm+8bhkFpaWlL247q6G0dwPu7D7Lr46MMHRTBssX/rIe/InIRBQDQt69nXHxZWZlX7ePi4igsLCQ3N7fN9wsKClruDuLi4jpcV0efAVz46b/0fAVr/99/d7gGEene9AzgCiUkJPD222/z8ccfe9V++vTp7Nq1i71797b5fvPrw4YNu6IRQGY8A1Dfv4i0RwGA53t0V69ezfbt28nMzGTcuHGXbH/LLbewbt06PvjgA/Ly8i6aDPbKK68AcOutt15RXR3p21Pfv4i9XMkzAAwxDMMwbr/9dgMwRowYYXz44Yet3nO73caTTz5pVFRUtLyWkpJiAMaMGTOMr776yjAMw2hsbDRWr15tAEZoaKhx+vTpLj0HwzCMHR99Yjy87mXjP367yWhqaury44tIz6F5AP9w/vx5Fi5cyIcffgh4um+uuuoqioqKKCwsxDAMSkpK6N+/PwBut5tZs2bxxRdfEBoaSnx8PEVFRRQVFREYGMibb77J7bff3qXn0LzmT11dPf9y8w0kxEV36fFFpGfRUhD/0LdvX/73f/+X9evX8+1vf5uqqiqOHTtGQEAAycnJrF+/Hpfr63V0hgwZwpEjR1ixYgVXXXUVx48fp6Ghge9///vs37+/yy/+oFm/IuIb3QH4kb2HPmPn/iPc8t3r9OlfRC5LAeBnamvrCA4O0rh/EbksBYCIiE3pGYCIiE0pAEREbEoBICJiUwoAERGbUgCIiNiUAkBExKYUACIiNqUAEBGxKQWAiIhNKQBERGxKASAiYlMKABERm1IAiIjYlAJARMSmFAAiIjalABARsSkFgIiITSkARERsSgEgImJTCgAREZtSAIiI2JQCQETEphQAIiI2pQAQEbEpBYCIiE0pAEREbEoBICJiUwoAERGbUgCIiNiUAkBExKYUACIiNqUAEBGxKQWAiIhNKQBERGxKASAiYlMKABERm1IAiIjYlAJARMSmFAAiIjb1/wEh6UsqBIcfmQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 472.747x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this circuit is explained in more detail later on.\n",
    "qc = QuantumCircuit(q, c)\n",
    "# create GHZ state\n",
    "qc.h(q[0]) #apply H-gate to the first qubit\n",
    "qc.cx(q[0],q[1]) #entangle the first two qubits\n",
    "qc.cx(q[0],q[2]) #entangle the first and the last qubit\n",
    "qc.barrier() #visual seperation (optional)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Erwin:  \n",
    "\"*The first gate we see in the circuit above is the H-gate which brings the qubit into a \n",
    "            Superposition. When measured it has a 50% probability of beeing 0 and a 50% probability of beeing 1.*\"\n",
    "\n",
    "\"*The other gates we see look different. They are called CNOT-gates and operate on 2 qubits. \n",
    "            The qubit with the dot is the control bit and the other one with the cross sign is the target \n",
    "            bit. If the control bit is one an X-gate is applied to the target bit. Otherwise nothing happens.*\"\n",
    "            \n",
    "(An X-gate cannot be found in the picture above. The X-gate is similar to a NOT-gate used on classical computers. When applied to a qubit in state $ \\;\\;|1\\rangle $ it becomes $ \\;\\;|0\\rangle $ and the other way around.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Erwin:  \"*On a Quantum Computer you can only measure what \n",
    "            points in the direction of the Z-axis. Therefore, we need to make the state vector point in the  direction to derive information about the X or Y basis. When you are asked for the color (corresponds to x value) of your qubit you need to apply an \n",
    "            H-gate and measure the state afterwards. Applying the H-gate turns your state vector 180° around the \n",
    "            Z-axis and 90° around the Y-axis and therefore, enables you to read out the X-value.* \n",
    "            \n",
    "*When asked for\n",
    "            the shape you apply the sdg-gate followed by an H-gate and measure afterwards. This corresponds to \n",
    "            a Y measurement (shape) as the sdg gate turns the object by 270° around the Z-axis so that the \n",
    "            shape of the object is now pointing towards X. When applying an H-gate afterwards, it turns the \n",
    "            object 180° around the Z-axis and 90° around the Y-axis so that it is now pointing towards Z which is the only axis we are able to measure.*\n",
    "            \n",
    "*You can try to reconstruct the movements of a single qubit using the visualization below. Whether \n",
    "            the top or bottom side of the dice is revealed in a measurement is randomly chosen. In the initial \n",
    "            GHZ-state the dice is pointing up with a black side so that a color is pointing towards X and a\n",
    "            shape towards Y.*\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![title](GHZGame/visualization.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Erwin:  \n",
    "\"*The results for each player seems to be perfectly random, but all three results in fact are \n",
    "            strongly correlated and not independent. This is caused by the entanglement. The Bloch Sphere\n",
    "            visualization can only be used for a single qubit, but not for the entire (entangled) system \n",
    "            of multiple qubits. However the so-called QSphere shows that the measurement results of the GHZ-State can only be |000> or |111> with equal probability:*\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x700 with 2 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = BasicAer.get_backend('statevector_simulator') # the device to run on\n",
    "result = execute(qc, backend).result()\n",
    "psi = Statevector.from_instruction(qc)\n",
    "plot_state_qsphere(psi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "To measure the Y-basis of a quantum state, the following quantum circuit can be used:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 389.136x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print (\"To measure the Y-basis of a quantum state, the following quantum circuit can be used:\")\n",
    "qc = QuantumCircuit(q, c) #create a new Quantum circuit\n",
    "# If measuring the X or Z-value, this step is not necessary:\n",
    "#apply sdg-gate to qubit 0. Vector moves 90° counterclockwise around the Z-axis (e.g. from y-basis to x-basis)\n",
    "qc.sdg(q[0]) \n",
    "# If measuring the Z-value, this step is not necessary:\n",
    "#apply H-gate to qubit 0. Vector moves 180° around the Z-axis and 90° around the Y-axis (e.g. from x-basis to z-basis)\n",
    "qc.h(q[0]) \n",
    "#create measurement gate for qubit 0\n",
    "qc.measure(q[0],c[0]) \n",
    "#draw the circuit\n",
    "qc.draw(output='mpl') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "    Can you modify the cell above to build a Quantum circuit that is suitable for an X measurement by \n",
    "    commenting out or deleting the line that is not necessary? \n",
    "\n",
    "    Can you do the same for a Z-measurement? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "    A quantum circuit that can be used when your team is asked for the XYY-values, therefore, could look like\n",
    "    this:\n",
    "    (XYY means that Alice (player 1) is asked for the color while Bob and you (player 2 and 3) are asked for \n",
    "    a shape.\n",
    "    1 -> red or star\n",
    "    0 -> blue or rectangle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 890.803x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c) #create a new Quantum circuit\n",
    "# create GHZ state\n",
    "qc.h(q[0]) #apply H-gate to the first qubit\n",
    "qc.cx(q[0],q[1]) #entangle the first two qubits\n",
    "qc.cx(q[0],q[2]) #entangle the first and the last qubit\n",
    "qc.barrier() #visual seperation (optional)\n",
    "\n",
    "# measure each qubit accordingly\n",
    "qc.h(q[0]) #apply H-gate to the first qubit (for x-value, player 1)\n",
    "qc.sdg(q[1]) #apply sdg-gate to the second qubit\n",
    "qc.h(q[1]) #apply H-gate to the second qubit (for y-value, player 2)\n",
    "qc.sdg (q[2]) #apply sdg-gate to the third qubit\n",
    "qc.h(q[2]) #apply H-gate to the third qubit (for y-value, player 3)\n",
    "qc.measure(q,c) #create measurement gates for all qubits\n",
    "qc.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "    In this case the measurement results are distributed as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x700 with 2 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c) #create a new Quantum circuit\n",
    "# create GHZ state\n",
    "qc.h(q[0]) #apply H-gate to the first qubit\n",
    "qc.cx(q[0],q[1]) #entangle the first two qubits\n",
    "qc.cx(q[0],q[2]) #entangle the first and the last qubit\n",
    "qc.barrier() #visual seperation (optional)\n",
    "\n",
    "# measure each qubit accordingly\n",
    "qc.h(q[0]) #apply H-gate to the first qubit (for x-value, player 1)\n",
    "qc.sdg(q[1]) #apply sdg-gate to the second qubit\n",
    "qc.h(q[1]) #apply H-gate to the second qubit (for y-value, player 2)\n",
    "qc.sdg (q[2]) #apply sdg-gate to the third qubit\n",
    "qc.h(q[2]) #apply H-gate to the third qubit (for y-value, player 3)\n",
    "qc.draw(output='mpl') #draw the circuit\n",
    "result = execute(qc, backend).result()\n",
    "psi = Statevector.from_instruction(qc)\n",
    "plot_state_qsphere(psi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# So now let's play again, using this new strategy\n",
    "\n",
    "To generate a random question execute the next cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The question your team is getting asked is:\n",
      "Shape, color, shape\n"
     ]
    }
   ],
   "source": [
    "question = randomQuestion()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Try to build a quantum circuit that can be used to answer these questions on the next slide and provide the right answers to your team members (if you need  help use the previous cells as examples or continue to the next cells):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 180.108x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c) #creates a new Quantum circuit\n",
    "\n",
    "#TODO: create GHZ-state (try not to use the predefined function)\n",
    "\n",
    "#TODO: apply gates according to the question above\n",
    "\n",
    "qc.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Now let's test your Quantum circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'000': 100}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# runs your quantum circuit 100 times on a simulator\n",
    "simulate(qc, q, c, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Now you can check your results for yourself. You get several different answers and this can be correct as the requirements of an even or uneven number of ones or zeros can be satisfied in multiple ways."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Do you think your answers were right? Check it here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hmmm... There might still be a mistake.\n"
     ]
    }
   ],
   "source": [
    "# compares whether the measurement results from your circuit correspond to the question asked\n",
    "circuitCheck(qc, q, c, question)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Need some help? \n",
    "(Otherwise skip this cell)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 807.192x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c) #create a new Quantum circuit\n",
    "\n",
    "#creates GHZ-state\n",
    "qc.h(q[0]) #apply H-gate to the first qubit\n",
    "qc.cx(q[0],q[1]) #entangle the first two qubits\n",
    "qc.cx(q[0],q[2]) #entangle the first and the last qubit\n",
    "qc.barrier() #visual seperation (optional)\n",
    "\n",
    "#TODO: apply gates according to the question above - choose the right ones\n",
    "qc.sdg(q[0]) #apply sdg-gate to the first qubit\n",
    "qc.h(q[0]) #apply H-gate to the first qubit\n",
    "qc.sdg(q[1]) #apply sdg-gate to the second qubit\n",
    "qc.h(q[1]) #apply H-gate to the second qubit\n",
    "#qc.sdg (q[2]) #apply sdg-gate to the third qubit\n",
    "qc.h(q[2]) #apply H-gate to the third qubit \n",
    "\n",
    "#Hint: only h-gate for x-value, both gates for y-value\n",
    "\n",
    "\n",
    "qc.measure(q,c) #create measurement gates for all qubits\n",
    "qc.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To check your answer return to the previous slide."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Copy the following code in the cell above:\n",
      "\n",
      "\n",
      "qc.sdg(q[0])\n",
      "qc.h(q[0])\n",
      "qc.h(q[1])\n",
      "qc.sdg(q[2])\n",
      "qc.h(q[2])\n"
     ]
    }
   ],
   "source": [
    "# prints out the correct code for your questions\n",
    "correctAnswer(question)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "You: \n",
    "\"*Cool it works, and with this Quantum strategy the team can always win, no matter which question is asked. But still I don't really understand why and how?!*\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Background Information"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Entangled qubits have a strong dependency. Therefore, their states cannot be described individually but only in a correlated manner.\n",
    "In the GHZ state, for example, when performing an XXX-measurement only the results $\\;\\; |000\\rangle, |011\\rangle,  |101\\rangle $ and $ \\;\\;|110\\rangle $ occur.\n",
    "The fascinating thing is each qubit when observed individually (for example when only looking at the first qubit), behaves perfectly random. But when considering the whole system a dependency becomes obvious. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "A commonly known entangled state is the Bell state.The state can be $\\;\\frac{|00\\rangle + |11\\rangle}{\\sqrt{2}}\\;\\;$. When measuring the first qubit in state 1 we can already say with certainty that the result of the second measurement will also be 1, as a state with mixed results cannot occur."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "But let's go back to our Experiment. We remember the GHZ-state from above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 472.747x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q,c)\n",
    "ghz_state(qc,q).draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Which outcomes do you expect when executing this circuit, using the z-axis as measurement basis?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a) All 8 possible states equally mixed (|000>, |001>, |010>, ..., |110>, |111>)\n",
      "(b) A random distribution across all 8 states (|000>, |001>, |010>, ..., |110>, |111>)\n",
      "(c) Measurement result in 50% is state |000> and in 50% is state |100>\n",
      "(d) Measurement result in 50% is state |000> and in 50% is state |111>\n",
      "No, try again!\n"
     ]
    }
   ],
   "source": [
    "quiz()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now try it out:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(simulate(qc, q, c, 100)) # Visualise the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Interestingly the only results that you get are either $ \\;\\;|000\\rangle $ or $ \\;\\;|111\\rangle $ with roughly 50/50 probability (Increase the number of shots to get more accurate results - closer to 50%).\n",
    "This is because q0 is brought into a superposition. In case it is 0 the two CNOT gates do not change the value of the other two qubits. If it is 1 both of the other values (which initially were 0) are flipped to 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "This becomes obvious when looking at the state which can be written as $\\;\\;|GHZ\\rangle=\\frac{|000\\rangle + |111\\rangle}{\\sqrt{2}}\\;\\;$ and only consists of these two basis states."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "And why can it be used to answer the questions of the experiment above?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "When measuring on the XXX-basis, we apply a Hadamard-gate to each of the qubits.\n",
    "A Hadamard-gate can be described with the following matrix:\n",
    "\n",
    "$$ H=\\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "If we want to apply the H-gate 3 times (one time on each qubit) we can use the tensor product. For the tensor product A⨂B each block aij*B is calculated. For the tensor product of three Hadamard gates this means:\n",
    "$$ H⨂H⨂H=\\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}⨂ \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}⨂ \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix} $$\n",
    "$$=  \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}⨂ \\frac 1 {\\sqrt{2}} \\begin{pmatrix} H & H \\\\ H & -H \\end{pmatrix}=   \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix} ⨂\\frac 1 {2}\\begin{pmatrix} 1 & 1 & 1 & 1 \\\\ 1 & -1 & 1 & -1 \\\\ 1 & 1 & -1 & -1 \\\\ 1 & -1 & -1 & 1 \\end{pmatrix}$$\n",
    "$$= \\frac 1 {2\\sqrt{2}} \\begin{pmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\\\ 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 \\\\ 1 & 1 & -1 & -1 & 1 & 1 & -1 & -1 \\\\ 1 & -1 & -1 & 1 & 1 & -1 & -1 & 1 \\\\ 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 \\\\ 1 & -1 & 1 & -1 & -1 & 1 & -1 & 1 \\\\ 1 & 1 & -1 & -1 & -1 & -1 & 1 & 1 \\\\ 1 & -1 & -1 & 1 & -1 & 1 & 1 & -1\\end{pmatrix}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The states $ \\;\\;|0\\rangle $ and $ \\;\\;|1\\rangle $ can also be represented by the vectors $ \\;\\;|0\\rangle=\\begin{pmatrix} 1 \\\\ 0\\end{pmatrix}|1\\rangle=\\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix} \\;\\;$\n",
    "\n",
    "Therefore, the GHZ state can also be represented as a vector:\n",
    "$$|GHZ\\rangle=\\frac{|000\\rangle + |111\\rangle}{\\sqrt{2}} = \\frac{|0\\rangle |0\\rangle |0\\rangle+ |1\\rangle |1\\rangle |1\\rangle}{\\sqrt{2}} $$\n",
    "$$ =\\frac {\\begin{pmatrix} 1 \\\\ 0\\end{pmatrix}⨂\\begin{pmatrix} 1 \\\\ 0\\end{pmatrix}⨂\\begin{pmatrix} 1 \\\\ 0\\end{pmatrix}+ \\begin{pmatrix} 0 \\\\ 1\\end{pmatrix}⨂\\begin{pmatrix} 0 \\\\ 1\\end{pmatrix}⨂\\begin{pmatrix} 0 \\\\ 1\\end{pmatrix}}{\\sqrt{2}}$$\n",
    "$$ =\\frac {\\begin{pmatrix} 1 \\\\ 0\\end{pmatrix}⨂\\begin{pmatrix} 1 \\\\ 0 \\\\ 0 \\\\ 0\\end{pmatrix}+ \\begin{pmatrix} 0 \\\\ 1\\end{pmatrix}⨂\\begin{pmatrix} 0 \\\\ 0\\\\ 0\\\\ 1\\end{pmatrix}⨂\\begin{pmatrix} 0 \\\\ 1\\end{pmatrix}}{\\sqrt{2}}$$\n",
    "$$ =\\frac 1 {\\sqrt{2}}\\left( {\\begin{pmatrix} 1 \\\\ 0 \\\\0 \\\\0 \\\\ 0\\\\ 0\\\\ 0 \\\\ 0\\end{pmatrix}+ \\begin{pmatrix} 0 \\\\ 0\\\\ 0\\\\ 0 \\\\0 \\\\0\\\\ 0\\\\ 1\\end{pmatrix}} \\right)\n",
    "= \\frac 1 {\\sqrt{2}} {\\begin{pmatrix} 1 \\\\ 0 \\\\0 \\\\0 \\\\ 0\\\\ 0\\\\ 0 \\\\ 1\\end{pmatrix}}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "When applying three Hadamard-gates to the GHZ state:\n",
    "$$\\frac 1 {2\\sqrt{2}} \\begin{pmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\\\ 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 \\\\ 1 & 1 & -1 & -1 & 1 & 1 & -1 & -1 \\\\ 1 & -1 & -1 & 1 & 1 & -1 & -1 & 1 \\\\ 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 \\\\ 1 & -1 & 1 & -1 & -1 & 1 & -1 & 1 \\\\ 1 & 1 & -1 & -1 & -1 & -1 & 1 & 1 \\\\ 1 & -1 & -1 & 1 & -1 & 1 & 1 & -1\\end{pmatrix}*\\frac 1 {\\sqrt{2}} {\\begin{pmatrix} 1 \\\\ 0 \\\\0 \\\\0 \\\\ 0\\\\ 0\\\\ 0 \\\\ 1\\end{pmatrix}}= \\frac 1 {4} {\\begin{pmatrix} 2 \\\\ 0 \\\\0 \\\\2 \\\\ 0\\\\ 2\\\\ 2 \\\\ 0\\end{pmatrix}} $$\n",
    "$$= \\frac 1 {4} (2*|000\\rangle+0*|001\\rangle+0*|010\\rangle+2*|011\\rangle+0*|100\\rangle+2*|101\\rangle+2*|110\\rangle+0*|111\\rangle)$$\n",
    "$$= \\frac 1 {2} (|000\\rangle+|011\\rangle+|101\\rangle+|110\\rangle)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "As expected only the results with an even number of ones occur."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "When measuring a Y-value we need an additional gate: $$ S^†= \\begin{pmatrix} 1 & 0 \\\\ 0 & -i \\end{pmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "For the YYX-measurement we would apply the sdg-gate to qubit 0 and 1 follwed by a Hadamard-gate on all three qubits. Therefore the following needs to be caluclated:\n",
    "\n",
    "$$HS^†⨂HS^†⨂H$$\n",
    "$$=\\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}\\begin{pmatrix} 1 & 0 \\\\ 0 & -i \\end{pmatrix}⨂ \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}\\begin{pmatrix} 1 & 0 \\\\ 0 & -i \\end{pmatrix}⨂ \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix} $$\n",
    "$$= \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & -i \\\\ 1 & i \\end{pmatrix}⨂ \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & -i \\\\ 1 & i \\end{pmatrix}⨂ \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "When applying this measurement to the GHZ state:\n",
    "\n",
    "$$HS^†⨂HS^†⨂H *\\frac 1 {\\sqrt{2}} {\\begin{pmatrix} 1 \\\\ 0 \\\\0 \\\\0 \\\\ 0\\\\ 0\\\\ 0 \\\\ 1\\end{pmatrix}}= \\frac 1 {4} {\\begin{pmatrix} 0 \\\\ 2 \\\\2 \\\\0 \\\\ 2\\\\ 0\\\\ 0 \\\\ 2\\end{pmatrix}} $$\n",
    "$$= \\frac 1 {4} (0*|000\\rangle+2*|001\\rangle+2*|010\\rangle+0*|011\\rangle+2*|100\\rangle+0*|101\\rangle+0*|110\\rangle+2*|111\\rangle)$$\n",
    "$$= \\frac 1 {2} (|001\\rangle+|010\\rangle+|100\\rangle+|111\\rangle)$$\n",
    "\n",
    "only the results with an even number of zeros, and accordingly an even number of blue or rectangle, remain."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "## What does it change?"
   ]
  },
  {
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   "source": [
    "As we saw above, any strategy that is using pre-defined answers (i.e. \"local hidden variables\") cannot answer all four sets of questions correctly. But the procedure based on quantum mechanics and Entaglement, i.e. the GHZ state, was able to give a correct answer all the time. \n",
    "\n",
    "How can that be explained? \n",
    "\n",
    "The final pragraphs of Mermin's book \"Quantum Computer Science: An Introduction\" conclude: \"The best explanation anybody has come up with to this day is to insist that no explanation is needed beyond what one can infer from the laws of quantum mechanics. Those laws are correct. (...) One gets puzzled only if one tries to understand how the rules can work not only for the actual situation in which they are applied, but also in alternative situations that might have been chosen but were not. (...) A good motto for the quantum physicist and for future quantum computer scientists might be 'What didn’t happen didn't happen.'\""
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   "source": [
    "To learn more about Quantum Entanglement you can look at the Hardy's paradox here: https://mybinder.org/v2/gh/JanLahmann/Fun-with-Quantum/master?filepath=Hardys-Paradox.ipynb\n",
    "\n",
    "One use case entanglement is needed for is the so-called \"Quantum Teleportation\". You can learn what it is and find out more about Quantum Entanglement here: https://qiskit.org/textbook/ch-algorithms/teleportation.html"
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