{
    "nbformat": 2, 
    "metadata": {
        "name": "dense_coding"
    }, 
    "worksheets": [
        {
            "cells": [
                {
                    "source": "<h1>Dense Coding\n</h1>", 
                    "cell_type": "markdown"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 2, 
                    "input": "%load_ext sympyprinting"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 3, 
                    "input": "from sympy import sqrt, symbols, Rational\nfrom sympy import expand, Eq, Symbol, simplify, exp, sin\nfrom sympy.physics.quantum import *\nfrom sympy.physics.quantum.qubit import *\nfrom sympy.physics.quantum.gate import *\nfrom sympy.physics.quantum.grover import *\nfrom sympy.physics.quantum.qft import QFT, IQFT, Fourier\nfrom sympy.physics.quantum.circuitplot import circuit_plot"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "pyout", 
                            "latex": "$$\\frac{1}{2} \\sqrt{2} {\\left|00\\right\\rangle } + \\frac{1}{2} \\sqrt{2} {\\left|11\\right\\rangle }$$", 
                            "prompt_number": 4, 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAALwAAAAkCAYAAAAzfFCFAAAABHNCSVQICAgIfAhkiAAABZRJREFU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\n0rjOgKiDGwAAAABJRU5ErkJggg==\n", 
                            "text": "\u23bd\u23bd\u23bd          \u23bd\u23bd\u23bd     \n\u2572\u2571 2 \u22c5\u275800\u27e9   \u2572\u2571 2 \u22c5\u275811\u27e9\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n    2            2"
                        }
                    ], 
                    "collapsed": false, 
                    "prompt_number": 4, 
                    "input": "psi = Qubit('00')/sqrt(2) + Qubit('11')/sqrt(2); psi\n"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [], 
                    "collapsed": true, 
                    "prompt_number": 5, 
                    "input": "circuits = [H(1)*CNOT(1,0), H(1)*CNOT(1,0)*X(1), H(1)*CNOT(1,0)*Z(1), H(1)*CNOT(1,0)*Z(1)*X(1)]"
                }, 
                {
                    "cell_type": "code", 
                    "language": "python", 
                    "outputs": [
                        {
                            "output_type": "display_data", 
                            "latex": "$$H_{1} CNOT_{1,0} \\left(\\frac{1}{2} \\sqrt{2} {\\left|00\\right\\rangle } + \\frac{1}{2} \\sqrt{2} {\\left|11\\right\\rangle }\\right) = {\\left|00\\right\\rangle }$$", 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAAWUAAAAmCAYAAAAcPorNAAAABHNCSVQICAgIfAhkiAAADH9JREFU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\ny/8BXM2fWYIlT5QAAAAASUVORK5CYII=\n", 
                            "text": "\u239b  \u23bd\u23bd\u23bd          \u23bd\u23bd\u23bd     \u239e       \n           \u239c\u2572\u2571 2 \u22c5\u275800\u27e9   \u2572\u2571 2 \u22c5\u275811\u27e9\u239f       \nH \u22c5CNOT   \u22c5\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f = \u275800\u27e9\n 1     1,0 \u239d    2            2     \u23a0"
                        }, 
                        {
                            "output_type": "display_data", 
                            "latex": "$$H_{1} CNOT_{1,0} X_{1} \\left(\\frac{1}{2} \\sqrt{2} {\\left|00\\right\\rangle } + \\frac{1}{2} \\sqrt{2} {\\left|11\\right\\rangle }\\right) = {\\left|01\\right\\rangle }$$", 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAAmCAYAAAAoR0vRAAAABHNCSVQICAgIfAhkiAAADRdJREFU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\nrkJggg==\n", 
                            "text": "\u239b  \u23bd\u23bd\u23bd          \u23bd\u23bd\u23bd     \u239e       \n              \u239c\u2572\u2571 2 \u22c5\u275800\u27e9   \u2572\u2571 2 \u22c5\u275811\u27e9\u239f       \nH \u22c5CNOT   \u22c5X \u22c5\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f = \u275801\u27e9\n 1     1,0  1 \u239d    2            2     \u23a0"
                        }, 
                        {
                            "output_type": "display_data", 
                            "latex": "$$H_{1} CNOT_{1,0} Z_{1} \\left(\\frac{1}{2} \\sqrt{2} {\\left|00\\right\\rangle } + \\frac{1}{2} \\sqrt{2} {\\left|11\\right\\rangle }\\right) = {\\left|10\\right\\rangle }$$", 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAAmCAYAAADKm1CoAAAABHNCSVQICAgIfAhkiAAADSdJREFU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\nL5K2XHBY3nYAAAAASUVORK5CYII=\n", 
                            "text": "\u239b  \u23bd\u23bd\u23bd          \u23bd\u23bd\u23bd     \u239e       \n              \u239c\u2572\u2571 2 \u22c5\u275800\u27e9   \u2572\u2571 2 \u22c5\u275811\u27e9\u239f       \nH \u22c5CNOT   \u22c5Z \u22c5\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f = \u275810\u27e9\n 1     1,0  1 \u239d    2            2     \u23a0"
                        }, 
                        {
                            "output_type": "display_data", 
                            "latex": "$$H_{1} CNOT_{1,0} Z_{1} X_{1} \\left(\\frac{1}{2} \\sqrt{2} {\\left|00\\right\\rangle } + \\frac{1}{2} \\sqrt{2} {\\left|11\\right\\rangle }\\right) = {\\left|11\\right\\rangle }$$", 
                            "png": 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4PB6Px+PxeDwej8fj8Xg8deK/A6n3/vuWvSEAAAAASUVORK5CYII=\n", 
                            "text": "\u239b  \u23bd\u23bd\u23bd          \u23bd\u23bd\u23bd     \u239e       \n                 \u239c\u2572\u2571 2 \u22c5\u275800\u27e9   \u2572\u2571 2 \u22c5\u275811\u27e9\u239f       \nH \u22c5CNOT   \u22c5Z \u22c5X \u22c5\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f = \u275811\u27e9\n 1     1,0  1  1 \u239d    2            2     \u23a0"
                        }, 
                        {
                            "output_type": "display_data", 
                            "png": "iVBORw0KGgoAAAANSUhEUgAAAJ8AAACOCAYAAAAvkdreAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAABtpJREFUeJzt3V9IU30cx/HPWbVo8iSN2lZIgyBoWMiCLHRrQ0pBrwqC\nLrrMrC6qiyCiiy4lSPpjzCTooqjoz9WCiv6wla4iizRzURDRIQjKihxrWuGvi+dJqv3RZzm/2zmf\nF5wbfzq+B9+dc3YaHk0pNQTgHxBNMU0ppaSHIHOySA9A5sX4SAzjIzGMj8QwPhLD+EgM4yMxjI/E\nMD4Sw/hIDOMjMYyPxDA+EsP4SAzjIzGMj8QwPhLD+EgM4yMxjI/EMD4Sw/hIDOMjMYyPxDA+EsP4\nSAzjKwF2ux2aphVss9vtIvvFv9VSAjRNQyF/TYV+/Wx45CMxjI/EML4St379eng8HlgsFlitVni9\nXrS0tAAAXr9+jbq6OlRUVMBisaC8vBzV1dUIhULCU/9HUdEb79d0//59pWma2rVrV8b11tZWpWma\nunDhQl6vXyg88hnAnTt3AACNjY0Z1yORCKZNm4b6+vqpHGtcpotvaGgI/f39SCQS0qNMmtu3b8Nq\ntcLn86Wtffv2DbFYDMuWLUN5ebnAdNmZJj6lFPbt2wen04na2lo4nU7s379f5BbDZBodHUUsFsOK\nFSswa9astPWenh58+fIFq1evFpguN9PEd/bsWRw5cgTDw8NIJBJIpVJoa2vDpUuXpEf7K319ffj8\n+TOCwWDG9UgkAgAIBAJTONXETJceYKq0t7cjmUz+9rVkMomjR49iw4YNQlP9vZ/Xe9evX8fDhw/T\n1nt6eqBpWlEe+bK+zQHArYi2bNatW6dmzJihkslk2tr379+VzWZTlZWVOd91Su1T1tOuUspQ24ED\nB9KuiWw2Gw4dOiQ+23hbrt9RV1cXqqqqYLPZ0tYfPXqEVCo1oaOexH6Z5ppv586dqKmpQVlZGQCg\nrKwMfr8f27dvF54sf/F4HB8+fIDf78+43t3dDaA4r/cAE73hmDlzJm7cuDF2AR6NRnHt2jVYrVbh\nyfL383ov0y0WAIjFYgBQnNd7MOmnWqQ+xZGvbPNu3LgRFy9exNu3b+FwONLWXS4XZs+ejRcvXuT1\n+oVmmiOf0YyMjCAajWLRokUZw+vr68O7d+9QW1srMN3EML4So+s6AoEAPB4P3r9/D13X4fP5cPz4\ncQDA5cuXUVNTg7Vr10LTNITDYQSDQdy9e1d48nQ87ZYAfpiUaJIxPhLD+EiMaf5vt9Rpmlaw154z\nZ07BXjsXxlcCSunN0f/B0y6JYXwkhvGRGMZHYhgfiWF8JIbxkRjGR2IYH4lhfCSG8ZEYxkdiGB+J\nYXwkhvGRGMZHYhgfiWF8JIbxkRjGR2IYH4lhfCSG8ZEYxkdiGB+JYXwkhvGRGMZHYhgfiWF8JIbx\nkRjGR2IYH4lhfCTGFPGNjIzg3LlzCAaDcDqdAP59NFRdXR3Onz+Pr1+/Ck9oToaOTymFtrY2uN1u\nnDx5Ejt27EBvby8A4PHjx9i2bRs6Ozvhdrtx+PBhw/7t42Jl2CcQjY6Oorm5GU+ePMHp06exZMmS\nsbU/n7gTj8exadMmVFdXIxQKwWIx9L/JomHY+Hbv3o0HDx7g6tWrY8/Y/SnT454SiQQaGhoQCATQ\n2to6laOaliHj6+/vR0NDA54+fQq73Z62nu1ZY4ODg1i6dCmi0ehvR0oqDEOeX0KhELZu3ZoxvFzm\nzp2LzZs3o6Ojo0CT0a8Md+QbGhqC2+3GwMAAFixYkPF7cj1lUdd1eL1e6LqedrqmyWW4I193dzeW\nL1+eNbzxLFy4EJWVlbh3794kT0Z/Mlx8nz59GruXly+Hw4GPHz9O0kSUTdbTbiEfNEcE5DjyKaVK\ncrt16xZWrlyZ83vG2z+v14uuri7xfTH6ZrjTrs/ng67riMfjef18b28vBgcHsWrVqkmejP5kuPis\nViuam5vzvl3S0dGBlpYWTJ/Op8EWmuFutQDAmzdvUFVVhVgslvFmcbZbLQMDA/D7/YjH43C5XFMx\nqqkZ7sgHABUVFTh48CAaGxvx6tWrCf3My5cv0dTUhPb2doY3VZSBHTt2TM2fP1+dOXNGDQ8Pj339\n191OpVLq1KlTyuVyqc7OTokxTcvQ8Sml1M2bN9WaNWuUw+FQe/fuVeFwWAFQ4XBY7dmzR82bN0/V\n19erSCQiParpGPKaL5Pnz5/jxIkTePbsGa5cuYKmpiZ4PB5s2bIFixcvlh7PlEwTHxUfQ77hoNLA\n+EgM4yMxjI/EMD4Sw/hIDOMjMYyPxDA+EsP4SAzjIzGMj8QwPhLD+EgM4yMxjI/EMD4Sw/hIDOMj\nMYyPxDA+EsP4SAzjIzGMj8QwPhLD+EgM4yMxjI/EMD4Sw/hIDOMjMYyPxDA+EsP4SAzjIzGMj8Qw\nPhLzA3qiBLIVwuRCAAAAAElFTkSuQmCC\n"
                        }, 
                        {
                            "output_type": "display_data", 
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                    ], 
                    "collapsed": false, 
                    "prompt_number": 6, 
                    "input": "for circuit in circuits:\n    circuit_plot(circuit, nqubits=2)\n    display(Eq(circuit*psi,qapply(circuit*psi)))"
                }
            ]
        }
    ]
}