Colab_06c_QKD.ipynb

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  "cells": [
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      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/EmmanueleVilla/quantum_computing/blob/main/Colab_06_QKD.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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          "name": "stdout",
          "text": [
            "Collecting qiskit\n",
            "  Downloading qiskit-0.43.2.tar.gz (9.1 kB)\n",
            "  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
            "  Installing backend dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Preparing metadata (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "Collecting qiskit-terra==0.24.1 (from qiskit)\n",
            "  Downloading qiskit_terra-0.24.1-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (5.9 MB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m5.9/5.9 MB\u001b[0m \u001b[31m62.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hCollecting qiskit-aer==0.12.1 (from qiskit)\n",
            "  Downloading qiskit_aer-0.12.1-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (12.8 MB)\n",
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            "\u001b[?25hCollecting qiskit-ibmq-provider==0.20.2 (from qiskit)\n",
            "  Downloading qiskit_ibmq_provider-0.20.2-py3-none-any.whl (241 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m241.5/241.5 kB\u001b[0m \u001b[31m26.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: numpy>=1.16.3 in /usr/local/lib/python3.10/dist-packages (from qiskit-aer==0.12.1->qiskit) (1.22.4)\n",
            "Requirement already satisfied: scipy>=1.0 in /usr/local/lib/python3.10/dist-packages (from qiskit-aer==0.12.1->qiskit) (1.10.1)\n",
            "Requirement already satisfied: requests>=2.19 in /usr/local/lib/python3.10/dist-packages (from qiskit-ibmq-provider==0.20.2->qiskit) (2.27.1)\n",
            "Collecting requests-ntlm<=1.1.0 (from qiskit-ibmq-provider==0.20.2->qiskit)\n",
            "  Downloading requests_ntlm-1.1.0-py2.py3-none-any.whl (5.7 kB)\n",
            "Requirement already satisfied: urllib3>=1.21.1 in /usr/local/lib/python3.10/dist-packages (from qiskit-ibmq-provider==0.20.2->qiskit) (1.26.16)\n",
            "Requirement already satisfied: python-dateutil>=2.8.0 in /usr/local/lib/python3.10/dist-packages (from qiskit-ibmq-provider==0.20.2->qiskit) (2.8.2)\n",
            "Requirement already satisfied: websocket-client>=1.5.1 in /usr/local/lib/python3.10/dist-packages (from qiskit-ibmq-provider==0.20.2->qiskit) (1.6.0)\n",
            "Collecting websockets>=10.0 (from qiskit-ibmq-provider==0.20.2->qiskit)\n",
            "  Downloading websockets-11.0.3-cp310-cp310-manylinux_2_5_x86_64.manylinux1_x86_64.manylinux_2_17_x86_64.manylinux2014_x86_64.whl (129 kB)\n",
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            "\u001b[?25hCollecting rustworkx>=0.12.0 (from qiskit-terra==0.24.1->qiskit)\n",
            "  Downloading rustworkx-0.13.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (1.9 MB)\n",
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            "\u001b[?25hCollecting ply>=3.10 (from qiskit-terra==0.24.1->qiskit)\n",
            "  Downloading ply-3.11-py2.py3-none-any.whl (49 kB)\n",
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            "Collecting dill>=0.3 (from qiskit-terra==0.24.1->qiskit)\n",
            "  Downloading dill-0.3.6-py3-none-any.whl (110 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m110.5/110.5 kB\u001b[0m \u001b[31m12.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hCollecting stevedore>=3.0.0 (from qiskit-terra==0.24.1->qiskit)\n",
            "  Downloading stevedore-5.1.0-py3-none-any.whl (49 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m49.6/49.6 kB\u001b[0m \u001b[31m6.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hCollecting symengine<0.10,>=0.9 (from qiskit-terra==0.24.1->qiskit)\n",
            "  Downloading symengine-0.9.2-cp310-cp310-manylinux2010_x86_64.whl (37.5 MB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m37.5/37.5 MB\u001b[0m \u001b[31m22.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.8.0->qiskit-ibmq-provider==0.20.2->qiskit) (1.16.0)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.10/dist-packages (from requests>=2.19->qiskit-ibmq-provider==0.20.2->qiskit) (2023.5.7)\n",
            "Requirement already satisfied: charset-normalizer~=2.0.0 in /usr/local/lib/python3.10/dist-packages (from requests>=2.19->qiskit-ibmq-provider==0.20.2->qiskit) (2.0.12)\n",
            "Requirement already satisfied: idna<4,>=2.5 in /usr/local/lib/python3.10/dist-packages (from requests>=2.19->qiskit-ibmq-provider==0.20.2->qiskit) (3.4)\n",
            "Collecting ntlm-auth>=1.0.2 (from requests-ntlm<=1.1.0->qiskit-ibmq-provider==0.20.2->qiskit)\n",
            "  Downloading ntlm_auth-1.5.0-py2.py3-none-any.whl (29 kB)\n",
            "Collecting cryptography>=1.3 (from requests-ntlm<=1.1.0->qiskit-ibmq-provider==0.20.2->qiskit)\n",
            "  Downloading cryptography-41.0.2-cp37-abi3-manylinux_2_28_x86_64.whl (4.3 MB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m4.3/4.3 MB\u001b[0m \u001b[31m81.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hCollecting pbr!=2.1.0,>=2.0.0 (from stevedore>=3.0.0->qiskit-terra==0.24.1->qiskit)\n",
            "  Downloading pbr-5.11.1-py2.py3-none-any.whl (112 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m112.7/112.7 kB\u001b[0m \u001b[31m14.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.10/dist-packages (from sympy>=1.3->qiskit-terra==0.24.1->qiskit) (1.3.0)\n",
            "Requirement already satisfied: cffi>=1.12 in /usr/local/lib/python3.10/dist-packages (from cryptography>=1.3->requests-ntlm<=1.1.0->qiskit-ibmq-provider==0.20.2->qiskit) (1.15.1)\n",
            "Requirement already satisfied: pycparser in /usr/local/lib/python3.10/dist-packages (from cffi>=1.12->cryptography>=1.3->requests-ntlm<=1.1.0->qiskit-ibmq-provider==0.20.2->qiskit) (2.21)\n",
            "Building wheels for collected packages: qiskit\n",
            "  Building wheel for qiskit (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for qiskit: filename=qiskit-0.43.2-py3-none-any.whl size=7640 sha256=319e5103e11f651b44aaad31ef5abc763d2086e53c7b1137a0b14ca71490720d\n",
            "  Stored in directory: /root/.cache/pip/wheels/d4/ad/4f/f54eb8743e54c5bab69837b842cf56a8a87ac7c57a2abf85ad\n",
            "Successfully built qiskit\n",
            "Installing collected packages: ply, websockets, symengine, rustworkx, pbr, ntlm-auth, dill, stevedore, cryptography, requests-ntlm, qiskit-terra, qiskit-ibmq-provider, qiskit-aer, qiskit\n",
            "Successfully installed cryptography-41.0.2 dill-0.3.6 ntlm-auth-1.5.0 pbr-5.11.1 ply-3.11 qiskit-0.43.2 qiskit-aer-0.12.1 qiskit-ibmq-provider-0.20.2 qiskit-terra-0.24.1 requests-ntlm-1.1.0 rustworkx-0.13.0 stevedore-5.1.0 symengine-0.9.2 websockets-11.0.3\n"
          ]
        }
      ],
      "source": [
        "!pip install qiskit"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install pylatexenc"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HknCEcDhUVs1",
        "outputId": "93713577-8c6b-4dd5-e8e6-7740a946ac3e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting pylatexenc\n",
            "  Downloading pylatexenc-2.10.tar.gz (162 kB)\n",
            "\u001b[?25l     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/162.6 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m162.6/162.6 kB\u001b[0m \u001b[31m5.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "Building wheels for collected packages: pylatexenc\n",
            "  Building wheel for pylatexenc (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for pylatexenc: filename=pylatexenc-2.10-py3-none-any.whl size=136820 sha256=49c7369b4d662fca80f1d5879aa6e112349e78caa8dcee7f245453d5b95d437c\n",
            "  Stored in directory: /root/.cache/pip/wheels/d3/31/8b/e09b0386afd80cfc556c00408c9aeea5c35c4d484a9c762fd5\n",
            "Successfully built pylatexenc\n",
            "Installing collected packages: pylatexenc\n",
            "Successfully installed pylatexenc-2.10\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import qiskit as qk\n",
        "from qiskit.tools.monitor import job_monitor\n",
        "from qiskit.visualization import plot_histogram, array_to_latex\n",
        "from qiskit.tools.visualization import plot_bloch_multivector\n",
        "import qiskit.tools.jupyter\n",
        "%matplotlib inline\n",
        "%qiskit_job_watcher"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 60,
          "referenced_widgets": [
            "35995519e4f040edb555d3509a77731a",
            "f31ca4a32ad74e9db4e974d60f43e13e",
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            "e132d59691684c9290d81e3f4edb6129",
            "ffc2ba9dbf244e79988b75a121b36010",
            "bbd5da547fa048e7911a288f7d329816",
            "1b8c1592777b4988a5d430d82995f9af",
            "abb86be01eec45b3a14f1e2b8da38c6f",
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            "c862b894e0b14413b37cf5420fa0c2df",
            "d5df0c64c73e452e941e9c2bfcda0dd8",
            "6e38e978565f4164a9209754e06e2029",
            "60d6de50e6fd458295ed2c07d21bbb02",
            "4bbffea65f7f4d62b572348c03a1bdc1",
            "37b9a6c51945450482012b7dbfb9388b",
            "15acc16b27f549df9c5e48c6d87e1bd2",
            "4915f089ed5c45a8ba020814ba4a0833"
          ]
        },
        "id": "2FOfB3UIUbpM",
        "outputId": "ddf730fb-1c5e-4afa-da19-cb112de615a4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Accordion(children=(VBox(layout=Layout(max_width='710px', min_width='710px')),), layout=Layout(max_height='500…"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "35995519e4f040edb555d3509a77731a"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ],
            "application/javascript": [
              "\n",
              "        const isLab = window['Jupyter'] === undefined;\n",
              "        const notebook = document.querySelector( isLab ? 'div.jp-Notebook' : '#site');\n",
              "        const jobWidget = document.querySelector('div.job_widget');\n",
              "        notebook.prepend(jobWidget);\n",
              "        jobWidget.style.zIndex = '999';\n",
              "        jobWidget.style.position = isLab ? 'sticky' : 'fixed';\n",
              "        jobWidget.style.boxShadow = '5px 5px 5px -3px black';\n",
              "        jobWidget.style.opacity = '0.95';\n",
              "        if (isLab) {\n",
              "            jobWidget.style.top = '0';\n",
              "            jobWidget.style.left = '0';\n",
              "        }\n",
              "        "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "quantum_simulator = qk.Aer.get_backend('qasm_simulator')\n",
        "quantum_simulator"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AaXqWqKDVRe6",
        "outputId": "4bdf8ccd-9e8a-490d-eb8e-db2db549bf97"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "QasmSimulator('qasm_simulator')"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "state_vector_simulator = qk.Aer.get_backend('statevector_simulator')\n",
        "state_vector_simulator"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "baZDJLw6VTCy",
        "outputId": "5db14130-0852-4ffa-9469-cbbe9ef5ae4b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "StatevectorSimulator('statevector_simulator')"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "qc = qk.QuantumCircuit(1, 1)\n",
        "qc.h(0)\n",
        "qc.barrier()\n",
        "qc.h(0)\n",
        "\n",
        "qc.draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 191
        },
        "id": "WXRproveUiz7",
        "outputId": "dd95086f-c0c7-4da7-fcd3-a767d7619079"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 352.675x200.667 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "job = qk.execute(qc, backend=state_vector_simulator)\n",
        "result = job.result()\n",
        "state_vector = result.get_statevector()\n",
        "state_vector"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2rGPtMECU2t0",
        "outputId": "6a5bf545-edba-486f-c8d2-3a52bfd191de"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Statevector([1.-6.123234e-17j, 0.+0.000000e+00j],\n",
            "            dims=(2,))\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "array_to_latex(state_vector, prefix=\"\\t{Statevector = }\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "S6qr00GAVYV6",
        "outputId": "51489eb3-6afd-4850-8cc4-15fc7da3778a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.Latex object>"
            ],
            "text/latex": "$$\n\t{Statevector = }\n\\begin{bmatrix}\n1 & 0  \\\\\n \\end{bmatrix}\n$$"
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "qc.measure(0,0)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VwZvCnDoVd7D",
        "outputId": "be1f46ad-f68c-426d-bd3b-29416eee6ede"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<qiskit.circuit.instructionset.InstructionSet at 0x7f9f9cccf7f0>"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "job = qk.execute(qc, backend=quantum_simulator, shots=1024)\n",
        "result = job.result()\n",
        "counts = result.get_counts()\n",
        "counts"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qWfHhGGNWLmK",
        "outputId": "126ec1bf-26b8-47c9-bd5e-e8201b7ea0e2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'0': 1024}"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plot_bloch_multivector(state_vector)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "id": "TzF9tjuSWNJS",
        "outputId": "0b7c54de-9064-4218-9532-ffd39560b0ab"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 480x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "qc = qk.QuantumCircuit(1, 1)\n",
        "qc.h(0)\n",
        "qc.barrier()\n",
        "qc.measure(0, 0)\n",
        "qc.barrier()\n",
        "qc.h(0)\n",
        "qc.measure(0, 0)\n",
        "qc.draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 191
        },
        "id": "Mu7ydnGBWSsq",
        "outputId": "bbffce57-b96c-46f6-b1d4-3c5d582718a9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 603.508x200.667 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "job = qk.execute(qc, backend=quantum_simulator, shots=1024)\n",
        "result = job.result()\n",
        "counts = result.get_counts()\n",
        "counts"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZB5IQb5DWkY5",
        "outputId": "288ad182-d312-4a06-f1a0-0e15104da79c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'0': 497, '1': 527}"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Invio messaggio tra Alice e Bob senza interferenza di Eve"
      ],
      "metadata": {
        "id": "rSf54D33Wwqm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "alice_bits = np.random.randint(0, 2, 100)\n",
        "print(alice_bits)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "l_8lBI7eWy8B",
        "outputId": "649bc793-5370-4825-e783-dfd6dbed9292"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 0 1 0 1 1 0 1 0 1 0\n",
            " 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0\n",
            " 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 1]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "alice_basis = np.random.randint(0, 2, 100)\n",
        "print(alice_basis)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ipq-5FGKW8Tg",
        "outputId": "477eec42-b4a8-4c17-f01f-3c28576a3874"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 0 1 0\n",
            " 0 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 0\n",
            " 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 1 1 0 0 0 0]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "bob_basis = np.random.randint(0, 2, 100)\n",
        "print(bob_basis)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9VDnZbKmYJh6",
        "outputId": "1c647840-0cc4-4a30-e546-152f026bc057"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0\n",
            " 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0\n",
            " 1 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def encode_message(bits, bases):\n",
        "  message = []\n",
        "  for i in range(len(bits)):\n",
        "    qc = qk.QuantumCircuit(1, 1)\n",
        "    if alice_basis[i] == 0: # Voglio misurare il cubit in verticale\n",
        "      if alice_bits[i] == 0:\n",
        "        pass\n",
        "      else:\n",
        "        qc.x(0)\n",
        "    else: # Voglio misurare il cubit in orizzontale\n",
        "      if alice_bits[i] == 0:\n",
        "        qc.h(0)\n",
        "      else:\n",
        "        qc.x(0)\n",
        "        qc.h(0)\n",
        "    qc.barrier()\n",
        "    message.append(qc)\n",
        "  return message"
      ],
      "metadata": {
        "id": "r4J3T-nyXA0A"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def measure_message(message, bases):\n",
        "  backend = qk.Aer.get_backend('aer_simulator')\n",
        "  measurements = []\n",
        "  for i in range(len(message)):\n",
        "    if bob_basis[i] == 0: # Voglio misurare il cubit in verticale\n",
        "      message[i].measure(0, 0)\n",
        "    else: # Voglio misurare il cubit in orizzontale\n",
        "      message[i].h(0)\n",
        "      message[i].measure(0, 0)\n",
        "    result = backend.run(message[i], shots=1, memory=True).result()\n",
        "    measured_bit = int(result.get_memory()[0])\n",
        "    measurements.append(measured_bit)\n",
        "  return measurements"
      ],
      "metadata": {
        "id": "nQusWns2X2WH"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def remove_wrong(a_basis, b_basis, bits):\n",
        "  good_bits = []\n",
        "  for i in range(len(bits)):\n",
        "    if a_basis[i] == b_basis[i]:\n",
        "      good_bits.append(bits[i])\n",
        "  return good_bits"
      ],
      "metadata": {
        "id": "KViaLUwlZuPm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "message = encode_message(alice_bits, alice_basis)\n",
        "len(message)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o4LDCmmgY5qN",
        "outputId": "2b9ff2bb-d8d2-452d-f638-46b0361331d8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "100"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "message[1].draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 191
        },
        "id": "82y1TvMaZBB9",
        "outputId": "e9a3ea67-3bd3-48d1-f76f-4ffe56317556"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 185.453x200.667 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "bob_results = measure_message(message, bob_basis)\n",
        "bob_results = np.asarray(bob_results)\n",
        "bob_results"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TwgppTURZH8N",
        "outputId": "120f472c-36d5-41c1-c9dc-d14d25a5fb9d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0,\n",
              "       1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0,\n",
              "       0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1,\n",
              "       0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1,\n",
              "       1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0])"
            ]
          },
          "metadata": {},
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "alice_key = remove_wrong(alice_basis, bob_basis, alice_bits)\n",
        "alice_key = np.asarray(alice_key)\n",
        "alice_key"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hc9BSDN7ZXOk",
        "outputId": "094ca98c-1a55-4221-f342-4dfdb293d156"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0,\n",
              "       0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1,\n",
              "       1, 0, 0, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "bob_key = remove_wrong(alice_basis, bob_basis, bob_results)\n",
        "bob_key = np.asarray(bob_key)\n",
        "bob_key"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "58WgzcCnaN38",
        "outputId": "d80da947-6b42-4d48-f8ef-038b19667283"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0,\n",
              "       0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1,\n",
              "       1, 0, 0, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "alice_key == bob_key"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fvTsWs44aZ-r",
        "outputId": "b6d22081-924c-4f50-c806-3af80d9e7132"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
              "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
              "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
              "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
              "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
              "        True,  True,  True])"
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Invio messaggio tra Alice e Bob e Eve intercetta"
      ],
      "metadata": {
        "id": "WvVhT7QIbMHq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "alice_bits = np.random.randint(0,2,50)\n",
        "alice_basis = np.random.randint(0,2,50)\n",
        "message = encode_message(alice_bits, alice_basis)\n",
        "\n",
        "eve_basis = np.random.randint(0,2,50)\n",
        "intercepted_message = measure_message(message, eve_basis)\n",
        "\n",
        "bob_basis = np.random.randint(0,2,50)\n",
        "bob_results = measure_message(message, bob_basis)\n",
        "\n",
        "alice_key = remove_wrong(alice_basis, bob_basis, alice_bits)\n",
        "alice_key = np.asarray(alice_key)\n",
        "\n",
        "bob_key = remove_wrong(alice_basis, bob_basis, bob_results)\n",
        "bob_key = np.asarray(bob_key)\n",
        "\n",
        "alice_key == bob_key"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "d87F7wkZbQP5",
        "outputId": "9cf252ef-d068-41e6-a693-f8a121105245"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([False,  True,  True,  True, False,  True,  True,  True,  True,\n",
              "        True,  True,  True,  True, False,  True, False, False,  True,\n",
              "        True,  True,  True,  True,  True])"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "wN9jEN2SbXlq"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}