Quantum_Teleportation_using_Quantum_Entanglement.ipynb

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        "<a href=\"https://colab.research.google.com/github/sabinthapa100/Quantum_Computing/blob/main/Quantum_Teleportation_using_Quantum_Entanglement.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# Using Entanglement For [Quantum Teleportation](https://www.ryanlarose.com/uploads/1/1/5/8/115879647/quic02.pdf) in Qiskit\n",
        "\n",
        "# [Entanglement](https://arxiv.org/abs/quant-ph/0603060)\n",
        "\n",
        "Entanglement is a quantum mechanical phenomenon in which two or more qubits can become linked in a way that their states become dependent on each other. This allows quantum computers to perform certain types of calculations that are not possible with classical computers. \n",
        "\n",
        "Entanglement occurs in two or more Hilbert spaces and is not possible on vectors(kets) of the same Hilbert space.\n",
        "\n",
        "Entanglement is a key ingredient in the quantum teleportation protocol, as it allows for the transfer of quantum information between two distant qubits.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## [Quantum Teleportation](https://arxiv.org/abs/quant-ph/9906110)\n",
        "\n",
        "Quantum teleportation is a protocol that allows the state of a qubit to be transferred from one location to another **without the physical transfer of the qubit itself**. Entanglement is a key ingredient in this protocol, as it allows for the transfer of quantum information between two distant qubits.\n",
        "\n",
        "\n",
        "More refs: [ref1](https://journals.aps.org/pra/pdf/10.1103/PhysRevA.58.4394?casa_token=kMU5TMvwfkYAAAAA%3Avs21c23AvxSnnUCliFV3l_MWBCZ8vAsXVrXz2V1uGJ8yesnECFzDF56dDOeSY1awszdzttAM5OyBFoQ), [ref2](https://arxiv.org/abs/quant-ph/0302030)"
      ],
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      "source": [
        "## [Steps in Quantum Teleportation](https://learn.qiskit.org/course/ch-algorithms/quantum-teleportation)\n",
        "\n",
        "To understand quantum teleportation, let's consider **a famous but Quantum** Nepali example of **Ram, Shyam and Hari** --- \"Hari wants to send a gift (**a quantum gift** - a quantum state $𝝭$  that are entangled, and are held in **Ram's lab** and **Shyam's lab**). \n",
        "\n",
        "### Actually, *Ram and Shyam* are \"**Mits (मित): their qubit states are entangled (one is from Rara, another is from Solu), quantum-lly**!\"\n",
        "\n",
        " **Hari** can send his gift $𝝭$ from **Rara** that is **Ram's lab: like quantum- telephone booth that prepares** to **Shyam's lab: quantum telephone booth** *quantum-mechanically* -- using their strength: **entanglement (मित)** -- the process is called **Quantum Teleportation**!\n",
        "\n",
        "The process involves following steps (in detail with mathematics and circuit/code/explaination involved)!"
      ],
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      "cell_type": "markdown",
      "source": [
        "**First of all, let's prepare ourselves for quantum setup!!!**\n",
        "\n",
        "Nothing to be memorized!!!\n",
        "\n",
        "Let's import all the libraries needed for this task!!!\n",
        "\n"
      ],
      "metadata": {
        "id": "geEDq-W0mHco"
      }
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    {
      "cell_type": "code",
      "source": [
        "#install qiskit \n",
        "!pip install qiskit\n",
        "\n",
        "#from qiskit, import all the needed libraries\n",
        "from qiskit import QuantumCircuit, transpile, QuantumRegister, ClassicalRegister, execute, Aer, IBMQ, BasicAer\n",
        "from qiskit.tools.jupyter import *\n",
        "from qiskit.visualization import *\n",
        "from qiskit.visualization import plot_histogram\n",
        "from qiskit.circuit.random import random_circuit\n",
        "from qiskit.quantum_info import Statevector, partial_trace, state_fidelity\n",
        "\n",
        "import numpy as np\n",
        "import math\n",
        "\n",
        "from qiskit.quantum_info import Statevector\n",
        "from qiskit.visualization import plot_bloch_multivector\n",
        "\n",
        "from qiskit.visualization import visualize_transition # We will use this function to run our circuit and visualize its final state\n",
        "\n",
        "from numpy.random import randint\n",
        "from random import random\n",
        "import matplotlib.pyplot as plt\n",
        "import math\n",
        "\n",
        "\n",
        "import warnings  # We are using this library to suppress some warning messages\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "\n",
        "#provider = IBMQ.load_account()\n",
        "\n",
        "print(\"Libraries Imported Successfully!\")"
      ],
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          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
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            "Libraries Imported Successfully!\n"
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      "cell_type": "markdown",
      "source": [
        "### Step 1:\n",
        "\n",
        "Ram and Shyam share **a Bell pair** (**entanglement (मित)को चिनारी बेल**)!"
      ],
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      "source": [
        "# Let's prepare 3 qubits and 3 classical bit circuit\n",
        "\n",
        "qc = QuantumCircuit(3,3)\n",
        "\n",
        "#where,\n",
        "# q0 = 𝝭 = Hari's gift for Shyam, sending from Ram's lab\n",
        "# q1 = Ram's qubit (tool to send Hari's gift - to Shyam!!!!) - in Ram's quantum booth!!!\n",
        "# q2 = Shyam's qubit - in Shyam's quantum booth (receives the gift 𝝭)!!!\n",
        "\n",
        "# Mits (मित)'s qubits need to be entangled (by using their quantum strength - \n",
        "# yes - Nepal can also have it! ;-))\n",
        "qc.h(1)\n",
        "qc.cx(1,2)\n",
        "\n",
        "\n",
        "#making a barrier and seeing the circuit\n",
        "qc.barrier()\n",
        "qc.draw()"
      ],
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          "base_uri": "https://localhost:8080/"
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        "id": "S7carf5-mfj_",
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          "output_type": "execute_result",
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              "                ░ \n",
              "q_0: ───────────░─\n",
              "     ┌───┐      ░ \n",
              "q_1: ┤ H ├──■───░─\n",
              "     └───┘┌─┴─┐ ░ \n",
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      "cell_type": "markdown",
      "source": [
        "### Step 2: **Hari asks Ram** to prepare **a gift** (𝝭) in his booth!"
      ],
      "metadata": {
        "id": "vbFzqzdHmFBt"
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    },
    {
      "cell_type": "code",
      "source": [
        "#Let's say Ram want's to send 𝝭 = q0 = any state!\n",
        "#q0 is initialized at |0> (by default in Qiskit) state - \n",
        "#which can be rotated by x-gate to get |1> state\n",
        "\n",
        "#&&&&&&======[this will prepare the gift in |1> state]=======\n",
        "q0 = qc.x(0) \n",
        "\n",
        "\n",
        "\n",
        "#&&&&&&&===we can define an amplitude (of a quantum state)===UNCOMMENT (two code lines) to play!\n",
        "#amplitude_0 = (0.5)**(1/2)\n",
        "\n",
        "#==prepares any state you wanna send===\n",
        "#qc.prepare_state([amplitude_0, (1 - amplitude_0**2)**(1/2)], 0) \n",
        "\n",
        "\n",
        "\n",
        "#make a barrier to visualize the circuit better\n",
        "qc.barrier()\n",
        "qc.draw()"
      ],
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      "cell_type": "markdown",
      "source": [
        "### Step 3: **Ram** packs the gift: (𝝭) (using Bell state): then he measures (checks) his half of **the Bell pair** and his special state in the \"Bell basis\"!\n",
        "\n",
        "\n",
        " **Ram packs Hari's gift into a quantum packet: qubit and checks if it's alright!**"
      ],
      "metadata": {
        "id": "rylMdQQKn05T"
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    },
    {
      "cell_type": "code",
      "source": [
        "#packing the gift (𝝭) that is entangling 𝝭 with Ram's qubit\n",
        "qc.cx(0,1)\n",
        "qc.h(0)\n",
        "\n",
        "#measuring Ram's state in the Bell basis: making sure all good!\n",
        "qc.measure([0,1], [0,1]) \n",
        "\n",
        "\n",
        "#for us to see their activities closely!\n",
        "qc.barrier()\n",
        "qc.draw(cregbundle = False) \n",
        "\n",
        "#using google:\n",
        "#to visualize the quantum circuit qc without bundling \n",
        "#the classical registers"
      ],
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          "metadata": {},
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    },
    {
      "cell_type": "markdown",
      "source": [
        "### Step 4: **Ram calls (sends the classical information: \"what's the gift?\" info) Shyam over a classical channel**!"
      ],
      "metadata": {
        "id": "_FTg-Autn1Xg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Step 5: Shyam make adjustment of his half of the Bell pair in his quantum booth based on the Ram's call (measurement results - classical!!!) \n",
        "\n",
        "This quantum adjustments needed in the quantum circuit:\n",
        "\n",
        "\n",
        "*   If the *Ram's measurement result* was 1, **apply an X-gate to Shyam's qubit** (Bell state)!\n",
        "\n",
        "* If the *gift (𝝭: teleportation qubit: q0)* was 1, **apply a Z-gate to the Shyam's qubit**! \n",
        "\n",
        "* Then measure Shyam's qubit!\n",
        "\n",
        "* Gift delivered? (need to confirm!!!)"
      ],
      "metadata": {
        "id": "mzXzjtWEoOU7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "qc.x(2).c_if(qc.clbits[1], 1)\n",
        "qc.z(2).c_if(qc.clbits[0], 1)\n",
        "\n",
        "#measuring Shyam's quit and storing it in 2nd classical bit\n",
        "qc.measure(2,2) \n",
        "\n",
        "qc.draw(cregbundle = False)"
      ],
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        "id": "hNuTCbCst4Hc",
        "outputId": "2fae896e-1911-477a-8123-669a4e01e503"
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            "text/plain": [
              "                ░ ┌───┐ ░      ┌───┐┌─┐ ░              \n",
              "q_0: ───────────░─┤ X ├─░───■──┤ H ├┤M├─░──────────────\n",
              "     ┌───┐      ░ └───┘ ░ ┌─┴─┐└┬─┬┘└╥┘ ░              \n",
              "q_1: ┤ H ├──■───░───────░─┤ X ├─┤M├──╫──░──────────────\n",
              "     └───┘┌─┴─┐ ░       ░ └───┘ └╥┘  ║  ░ ┌───┐┌───┐┌─┐\n",
              "q_2: ─────┤ X ├─░───────░────────╫───╫──░─┤ X ├┤ Z ├┤M├\n",
              "          └───┘ ░       ░        ║   ║  ░ └─╥─┘└─╥─┘└╥┘\n",
              "c_0: ════════════════════════════╬═══╩══════╬════■═══╬═\n",
              "                                 ║          ║        ║ \n",
              "c_1: ════════════════════════════╩══════════■════════╬═\n",
              "                                                     ║ \n",
              "c_2: ════════════════════════════════════════════════╩═\n",
              "                                                       "
            ],
            "text/html": [
              "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">                ░ ┌───┐ ░      ┌───┐┌─┐ ░              \n",
              "q_0: ───────────░─┤ X ├─░───■──┤ H ├┤M├─░──────────────\n",
              "     ┌───┐      ░ └───┘ ░ ┌─┴─┐└┬─┬┘└╥┘ ░              \n",
              "q_1: ┤ H ├──■───░───────░─┤ X ├─┤M├──╫──░──────────────\n",
              "     └───┘┌─┴─┐ ░       ░ └───┘ └╥┘  ║  ░ ┌───┐┌───┐┌─┐\n",
              "q_2: ─────┤ X ├─░───────░────────╫───╫──░─┤ X ├┤ Z ├┤M├\n",
              "          └───┘ ░       ░        ║   ║  ░ └─╥─┘└─╥─┘└╥┘\n",
              "c_0: ════════════════════════════╬═══╩══════╬════■═══╬═\n",
              "                                 ║          ║        ║ \n",
              "c_1: ════════════════════════════╩══════════■════════╬═\n",
              "                                                     ║ \n",
              "c_2: ════════════════════════════════════════════════╩═\n",
              "                                                       </pre>"
            ]
          },
          "metadata": {},
          "execution_count": 83
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Final Check: Simulation and Plot and Confirmation!!!\n",
        "\n",
        "**In Shyam's quantum booth!!!!**"
      ],
      "metadata": {
        "id": "3dV_VCdnuNfz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Simulation and plot of histogram results\n",
        "\n",
        "#using simulator\n",
        "backend = Aer.get_backend('qasm_simulator')  \n",
        "#(you can choose to use real quantum computer in ibm quantum lab!)\n",
        "\n",
        "job = execute(qc, backend = backend, shots = 1024)\n",
        "\n",
        "result = job.result()\n",
        "counts = result.get_counts()\n",
        "\n",
        "plot_histogram(counts)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pdDsosTGubw2",
        "outputId": "601d1c55-4b5e-4bdb-db0d-08f6e4209515"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 700x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 84
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Shyam's State: let's forget what Ram said (Ram's measurement result)\n",
        "\n",
        "shyam_state = [0, 0]\n",
        "for state in result.get_counts().keys():\n",
        "  shyam_state[int(state[0])] += result.get_counts()[state]\n",
        "\n",
        "norm = (sum(c**2 for c in shyam_state))**(1/2)\n",
        "shyam_state = [c / norm for c in shyam_state]\n",
        "\n",
        "statevector = Statevector(shyam_state)\n",
        "\n",
        "statevector.draw(output = 'latex')\n",
        "\n",
        "statevector.draw(output = 'bloch')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wcCiiFwWukIc",
        "outputId": "caca8e3f-4918-4764-f750-460e819271bd"
      },
      "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": 85
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Mathematical Steps of Quantum Teleportation\n",
        "\n",
        "The mathematical steps involved in the quantum teleportation are:\n",
        "\n"
      ],
      "metadata": {
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      }
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    {
      "cell_type": "markdown",
      "source": [
        "**Step 1: Ram and Shyam share a pair of entangled qubits (|$\\Phi^+$ ⟩) in the Bell state:**\n",
        "\n",
        "\n",
        "After applying H on q1 = |0⟩, we get a superposition state:\n",
        "\n",
        "\\begin{align}\n",
        "H |0⟩ &= \\frac{1}{\\sqrt{2}}\\begin{pmatrix}\n",
        "1 & 1 \\\\\n",
        "1 & -1\n",
        "\\end{pmatrix} \\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix} = \\frac{1}{\\sqrt{2}} \\begin{pmatrix} 1 \\\\ 1 \\end{pmatrix}\n",
        "\\end{align}\n",
        "\n",
        "\n",
        "and then applying CNOT[q1,q2], we obtain (in the Bell basis {|00⟩, |01⟩, |10⟩, |11⟩}: \n",
        "\\begin{equation}\n",
        "|\\Phi^+⟩ = \\frac{(|00⟩ + |11⟩)}{\\sqrt{2}}\n",
        "\\end{equation}\n",
        "\n",
        "That is to say:\n",
        "\n",
        "\\begin{align}\n",
        "|\\Phi^+ ⟩ &= \\frac{1}{\\sqrt{2}}(|0\\rangle \\otimes |0\\rangle + |1\\rangle \\otimes |1 \\rangle) \\\\\n",
        "&= \\frac{1}{\\sqrt{2}} \\begin{pmatrix}\n",
        "1 \\\\ 0 \\\\ 0 \\\\ 0\n",
        "\\end{pmatrix} + \\frac{1}{\\sqrt{2}} \\begin{pmatrix}\n",
        "0 \\\\ 0 \\\\ 0 \\\\ 1\n",
        "\\end{pmatrix} \\\\\n",
        "&= \\frac{1}{\\sqrt{2}} \\begin{pmatrix}\n",
        "1 \\\\ 0 \\\\ 0 \\\\ 1\n",
        "\\end{pmatrix} \\\\\n",
        "&= \\frac{1}{\\sqrt{2}} (|00⟩ + |11⟩) \\, \\, [in \\ the \\ computational \\ basis]\n",
        "\\end{align}\n",
        "\n",
        "The state $|\\Phi^+\\rangle$ is entangled because it cannot be written as the tensor product of two separate qubits.\n",
        "\n",
        "Specifically, $|\\Phi^+\\rangle$ is a maximally entangled state of two qubits, meaning that it has the highest possible degree of entanglement for a two-qubit state. In this case, the state $|\\Phi^+\\rangle$ is entangled because it has a non-zero amplitude for both of the possible states where one qubit is in the $|0\\rangle$ state and the other qubit is in the $|1\\rangle$ state, as well as for the states where the qubits are flipped.\n",
        "\n",
        "This entanglement means that the two qubits in the state $|\\Phi^+\\rangle$ are strongly correlated with each other, and measuring one of the qubits can affect the state of the other qubit in a non-trivial way.\n",
        "\n",
        "\n",
        "**Want to learn more?**\n",
        "\n",
        "In quantum mechanics, it is possible to have a composite system made up of two or more individual quantum systems. For example, two electrons can be combined to form a two-electron system, or two photons can be combined to form a two-photon system.\n",
        "\n",
        "When we have a composite quantum system, the state of the system can be described using a mathematical object called a state vector, which is an element of a vector space called the Hilbert space.\n",
        "\n",
        "In the case of a two-qubit system, the Hilbert space is the tensor product of the individual qubit Hilbert spaces. The tensor product operation combines the states of the two qubits into a single, composite state.\n",
        "\n",
        "If the two qubits are in a product state, meaning that they are not entangled with each other, then the state of the composite system can be written as the tensor product of the individual qubit states.\n",
        "\n",
        "However, if the two qubits are entangled with each other, then the state of the composite system cannot be written as a tensor product of the individual qubit states. In other words, the two qubits are not separable from each other, and measuring one qubit can affect the state of the other qubit in a non-trivial way.\n",
        "\n",
        "In the case of the state $|\\Phi^+\\rangle$, it cannot be written as a tensor product of two separate qubits, so it is an entangled state.\n",
        "\n",
        "\n"
      ],
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        "id": "_fD2fJed4h4_"
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    },
    {
      "cell_type": "markdown",
      "source": [
        "**Note1 : Qubits in : {|0⟩, |1⟩} basis:**\n",
        "\n",
        "***|0> State***\n",
        "\\begin{equation}\n",
        "|0\\rangle = 1|0\\rangle + 0|1\\rangle = \\begin{pmatrix} 1 \\\\ 0 \\\\ \\end{pmatrix}\n",
        "\\end{equation}\n",
        "\n",
        "***|1> State***\n",
        "\\begin{equation}\n",
        "|1\\rangle = 0|0\\rangle + 1|1\\rangle = \\begin{pmatrix} 0 \\\\ 1 \\\\ \\end{pmatrix}\n",
        "\\end{equation}\n",
        "\n",
        "**Note 2: [Tensor Products](https://www.ryanlarose.com/uploads/1/1/5/8/115879647/quic02.pdf): in the Bell basis: {|00⟩,|01⟩,|10⟩,|11⟩}:**\n",
        "\\begin{align}\n",
        "|0\\rangle \\otimes |1\\rangle &= \\begin{pmatrix}\n",
        "1 \\\\ 0\n",
        "\\end{pmatrix} \\otimes \\begin{pmatrix}\n",
        "0 \\\\ 1\n",
        "\\end{pmatrix} = \\begin{pmatrix}\n",
        "1 \\cdot \\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix} \\\\\n",
        "0 \\cdot \\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix}\n",
        "\\end{pmatrix} = \\begin{pmatrix}\n",
        "0 \\\\ 1 \\\\ 0 \\\\ 0\n",
        "\\end{pmatrix} \\\\\n",
        "\\end{align}\n",
        "\n",
        "This can be written in the Bell basis, that is to say,\n",
        "\\begin{align}\n",
        "|0\\rangle \\otimes |1\\rangle = \\begin{pmatrix}\n",
        "0 \\\\ 1 \\\\ 0 \\\\ 0\n",
        "\\end{pmatrix} = 0 |00⟩ + 1|01⟩ + 0 |10⟩ + 0 |11⟩.\n",
        "\\end{align}\n",
        "\n",
        "Similarly,\n",
        "\\begin{align}\n",
        "|1\\rangle \\otimes |0\\rangle &= \\begin{pmatrix}\n",
        "0 \\\\ 1\n",
        "\\end{pmatrix} \\otimes \\begin{pmatrix}\n",
        "1 \\\\ 0\n",
        "\\end{pmatrix} = \\begin{pmatrix}\n",
        "0 \\cdot \\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix} \\\\\n",
        "1 \\cdot \\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix}\n",
        "\\end{pmatrix} = \\begin{pmatrix}\n",
        "0 \\\\ 0 \\\\ 1 \\\\ 0\n",
        "\\end{pmatrix}  \\\\\n",
        "&= 0 |00⟩ + 0|01⟩ + 1|10⟩ + 0 |11⟩.\n",
        "\\end{align}\n",
        "\n",
        "\\begin{align}\n",
        "|0\\rangle \\otimes |0\\rangle &= \\begin{pmatrix}\n",
        "1 \\\\ 0\n",
        "\\end{pmatrix} \\otimes \\begin{pmatrix}\n",
        "1 \\\\ 0\n",
        "\\end{pmatrix} = \\begin{pmatrix}\n",
        "1 \\cdot \\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix} \\\\\n",
        "0 \\cdot \\begin{pmatrix} 1 \\\\ 0 \\end{pmatrix}\n",
        "\\end{pmatrix} = \\begin{pmatrix}\n",
        "1 \\\\ 0 \\\\ 0 \\\\ 0\n",
        "\\end{pmatrix}  \\\\\n",
        "&= 1 |00⟩ + 0|01⟩ + 0|10⟩ + 0 |11⟩.\n",
        "\\end{align}\n",
        "\n",
        "\n",
        "\\begin{align}\n",
        "|1\\rangle \\otimes |1\\rangle &= \\begin{pmatrix}\n",
        "0 \\\\ 1\n",
        "\\end{pmatrix} \\otimes \\begin{pmatrix}\n",
        "0 \\\\ 1\n",
        "\\end{pmatrix} = \\begin{pmatrix}\n",
        "0 \\cdot \\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix} \\\\\n",
        "1 \\cdot \\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix}\n",
        "\\end{pmatrix} = \\begin{pmatrix}\n",
        "0 \\\\ 0 \\\\ 0 \\\\ 1\n",
        "\\end{pmatrix}  \\\\\n",
        "&= 0 |00⟩ + 0|01⟩ + 0|10⟩ + 1|11⟩.\n",
        "\\end{align}\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "tXFqxeEJ9gnC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Step 2: Ram prepares (in his Quantum lab) the qubit (the gift) he wants to teleport ($|\\Psi$ ⟩):**\n",
        "\n",
        "\\begin{equation}\n",
        "|\\Psi \\rangle = \\alpha |0\\rangle + \\beta |1\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\\\ \\end{pmatrix}\n",
        "\\end{equation}\n",
        "\n",
        "Here, $|\\Psi>$ represents the qubit that Ram wants to teleport (**Hari's gift!!!**), with different amplitudes ($|α|^2$ and $|β|^2$) follow Born's rule: $\\sqrt{|α|^2 + |β|^2} = 1$."
      ],
      "metadata": {
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    },
    {
      "cell_type": "markdown",
      "source": [
        "**Step 3: Ram applies a controlled operation (CNOT) on his qubit ($|\\Phi^+$⟩) and the qubit he wants to teleport ($|\\Psi$ ⟩), and then applies a Hadamard gate to his qubit:**\n",
        "\n",
        "\n",
        "Note that the state of **the entire system (Ram + Shyam's qubits)** is:\n",
        "(reading from left to right: left most = q0 (zeroth - teleportation qubit), then comes q1 (1st), then q2 (second), that is |q0 q1 q2⟩)\n",
        "\n",
        "\\begin{align}\n",
        "|𝜳_{entire}⟩ &=  |\\Psi⟩ ⊗ \\frac{1}{\\sqrt{2}}(|00⟩ + |11⟩) \\\\\n",
        "&= (\\alpha |0\\rangle + |1\\rangle) ⊗ \\frac{1}{\\sqrt{2}}(|00⟩ + |11⟩) \\\\\n",
        "&= \\frac{1}{\\sqrt{2}} (α |000⟩ + α |011⟩ + β |100⟩ + β |111⟩).\n",
        "\\end{align}\n",
        "\n",
        "Here, $|\\Psi⟩$ represents the qubit that Ram wants to teleport (**Hari's gift!!!**), which is being entangled to the Bell state ($|\\Phi^+⟩$). In order to do that, first, we apply CNOT gate from  $|\\Psi⟩$ to $|\\Phi^+⟩$, and finally apply Hadamard gate (H) to the first qubit of the $|\\Psi⟩$.\n",
        "\n",
        "\n",
        "Applying CNOT gate to the |𝜳_{entire}⟩, which perform between the zeroth (teleporting qubit) and the first qubits (sending qubit) **[first (control) qubit never changes in CNOT gate; if control is |0⟩, the target doesnot get changed; but if the control qubit is |1⟩,then apply X to the target qubit \\]**, then we get\n",
        "\n",
        "\\begin{align}\n",
        "& CX|q_0, q_1⟩ = CX|𝜳_{entire}⟩  \\\\\n",
        "&= \\frac{1}{\\sqrt{2}} CX_{q_0,q_1}(α |000⟩ + α |011⟩ + β |100⟩ + β |111⟩) \\\\\n",
        "& = \\frac{1}{\\sqrt{2}} (α |000⟩ + α |011⟩ + β |110⟩ + β |101⟩)\n",
        "\\end{align}\n",
        "\n",
        "\n",
        "Now, performing a Hadamard gate on the zeroth qubit ($q_0$) to entangle with $q_1$, we get semi-final state |𝜳_{final}⟩:\n",
        "\n",
        "\\begin{align}\n",
        "|𝜳_{semi-final}⟩  &:= \\frac{1}{2} (α |000⟩ + α |100⟩ + α |011⟩ + α |111⟩ + β |010⟩ - β |110⟩ - β |101⟩ + β |001⟩ ) \\\\\n",
        "&:= \\frac{1}{2} (α |00⟩ |0⟩ + α |10⟩ |0⟩ + α |01⟩ |1⟩ + α |11⟩ |1⟩ + β |01⟩ |0⟩ - β |11⟩ |0⟩ - β |10⟩ |1⟩ + β |00⟩ |1⟩ ) \n",
        "\\end{align}\n",
        "\n",
        "\n",
        "There are four possibilities for the first two qubits ($q_0, q_1$): {|00⟩, |01⟩, |10⟩, |11⟩} -- computational basis. Grouping these two qubits together (rearranging these), we can get\n",
        "\n",
        "**(SEE SOME PATTERN???)**\n",
        "\\begin{align}\n",
        "|𝜳_{final}⟩  &:= \\frac{1}{2} |00\\rangle(\\alpha|0\\rangle + \\beta|1\\rangle) \\\\ \n",
        "&+ \\frac{1}{2} |01\\rangle(\\alpha|1\\rangle + \\beta|0\\rangle) \\\\\n",
        "&+ \\frac{1}{2} |10\\rangle(\\alpha|0\\rangle - \\beta|1\\rangle) \\\\\n",
        "&+ \\frac{1}{2}|11\\rangle(\\alpha|1\\rangle - \\beta|0\\rangle ).\n",
        "\\end{align}\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
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      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Step 3: Ram measures both of his qubits and sends the measurement results (two classical bits) to Shyam through classical communication.**\n",
        "\n",
        "Ram's measurement can be described by a projection operator, $M_{a,b} = |a\\rangle \\langle a| \\otimes |b\\rangle \\langle b|$, where $a,b \\in {0,1}$. Depending on the outcome of her measurement, Ram sends a message to Shyam indicating the measurement result.\n",
        "\n"
      ],
      "metadata": {
        "id": "BaOZ5Sla4h7r"
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    },
    {
      "cell_type": "markdown",
      "source": [
        "**Step 4: Based on the measurement results, Shyam applies a correction operation (X or Z gate) on his qubit to obtain the teleported state:**\n",
        "\n",
        "* If Ram's measurement results are |00⟩, Shyam performs nothing (or Identity - I).\n",
        "\n",
        "* If Ram's measurement results are |01⟩, Shyam applies an X gate to his qubit.\n",
        "\n",
        "* If Ram's measurement results are |10⟩, Shyam applies the Z gate to his qubit.\n",
        "\n",
        "* If Ram's measurement results are |11⟩, Shyam applies both the X and then Z gates to his qubit.\n",
        "\n",
        "This step can be represented mathematically as follows:\n",
        "\n",
        "\\begin{equation}\n",
        "|\\psi\\rangle = \\sum_{a,b} (-1)^{a \\cdot b} M_{a,b} (H \\otimes I) (CNOT \\otimes I) (|\\psi\\rangle \\otimes |\\Psi_{final}\\rangle)\n",
        "\\end{equation}\n",
        "\n",
        "Here, the $a \\cdot b$ term represents the inner product of the measurement results, and the correction gates are applied to Shyam's qubit based on the measurement results.\n",
        "\n"
      ],
      "metadata": {
        "id": "0OAo626-4iCK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Step 5: The teleported state is now stored in Shyam's qubit, and the original qubit held by Ram is destroyed.**\n",
        "\n",
        "Shyam's qubit now holds the teleported state |$\\Psi$⟩, which is identical to the original state held/teleported by Ram. Ram's qubit is destroyed during the process.\n",
        "\n",
        "Referring to the step 4 instructions, let's apply necessary gates: $I$, $X$, $Z$, or $X$ & $Z$, we get $|𝜳⟩$ (**intial qubit of Hari (teleportation qubit): the gift delivered!!!**)\n",
        "\n",
        "\\begin{align}\n",
        "& |𝜳_{final}⟩  = |\\Psi \\rangle = \\alpha |0\\rangle + \\beta |1\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\\\ \\end{pmatrix} \\\\ \n",
        "& |𝜳_{final}⟩ = I |𝜳_{final}⟩_{00} =  \\alpha |0\\rangle + \\beta |1\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\\\ \\end{pmatrix} = |\\Psi \\rangle \\\\\n",
        "& |𝜳_{final}⟩ = X |𝜳_{final}⟩_{01} = X (\\alpha|1\\rangle + \\beta|0\\rangle) = \\alpha |0\\rangle + \\beta |1\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\\\ \\end{pmatrix} = |\\Psi \\rangle \\\\\n",
        "& |𝜳_{final}⟩ = Z |𝜳_{final}⟩_{10} = Z \\rangle(\\alpha|0\\rangle - \\beta|1\\rangle) = \\alpha |0\\rangle + \\beta |1\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\\\ \\end{pmatrix} = |\\Psi \\rangle \\\\\n",
        "& |𝜳_{final}⟩ = ZX |𝜳_{final}⟩_{11} =  ZX (\\alpha|1\\rangle - \\beta|0\\rangle ) = Z(\\alpha|0\\rangle - \\beta|1\\rangle ) = \\alpha |0\\rangle + \\beta |1\\rangle = \\begin{pmatrix} \\alpha \\\\ \\beta \\\\ \\end{pmatrix} = |\\Psi \\rangle \\\\.\n",
        "\\end{align}\n",
        "\n",
        "Thus, quantum teleportation involves the use of entangled qubits and classical communication to transfer the state of a qubit from one physical location to another without physically transferring the qubit itself!"
      ],
      "metadata": {
        "id": "N1K0MVmu4iEy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "***Note 3: Quantum Gates (used here):***\n",
        "\n",
        "***Pauli X-gate (NOT gate, bit flip gate):***\n",
        "\\begin{equation}\n",
        "X = \\begin{pmatrix}\n",
        "0 & 1 \\\\\n",
        "1 & 0\n",
        "\\end{pmatrix}\n",
        "\\end{equation}\n",
        "\n",
        "\n",
        "\\begin{align}\n",
        "X|0\\rangle &= |1\\rangle \\\\\n",
        "X|1\\rangle &= |0\\rangle\n",
        "\\end{align}\n",
        "\n",
        "\n",
        "\n",
        "***Z-gate (rotation around Z axis by Π angle (180°), phase flip gate):***\n",
        "\\begin{align}\n",
        "Z = \\begin{pmatrix}\n",
        "1 & 0 \\\\\n",
        "0 & -1 \\\\\n",
        "\\end{pmatrix}\n",
        "\\end{align}\n",
        "\n",
        "\\begin{align}\n",
        "Z|0\\rangle &= \\begin{pmatrix}\n",
        "1 & 0 \\\\\n",
        "0 & -1 \\\\\n",
        "\\end{pmatrix} \\begin{pmatrix}\n",
        "1 \\\\\n",
        "0 \\\\\n",
        "\\end{pmatrix} = \\begin{pmatrix}\n",
        "1 \\\\\n",
        "0 \\\\\n",
        "\\end{pmatrix} = |0\\rangle \\\\\n",
        "Z|1\\rangle &= \\begin{pmatrix}\n",
        "1 & 0 \\\\\n",
        "0 & -1 \\\\\n",
        "\\end{pmatrix} \\begin{pmatrix}\n",
        "0 \\\\\n",
        "1 \\\\\n",
        "\\end{pmatrix} = \\begin{pmatrix}\n",
        "0 \\\\\n",
        "-1 \\\\\n",
        "\\end{pmatrix} = -|1\\rangle\n",
        "\\end{align}\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "***H-gate:***\n",
        "\\begin{equation}\n",
        "H = \\frac{1}{\\sqrt{2}}\\begin{pmatrix}\n",
        "1 & 1 \\\\\n",
        "1 & -1\n",
        "\\end{pmatrix}\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{align}\n",
        "H|0\\rangle &= \\frac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle) \\\\\n",
        "H|1\\rangle &= \\frac{1}{\\sqrt{2}}(|0\\rangle - |1\\rangle)\n",
        "\\end{align}\n",
        "\n",
        "\n",
        "***[Controlled-NOT Gate (CNOT): for multi-qubit gates](https://www.ryanlarose.com/uploads/1/1/5/8/115879647/quic02.pdf):***\n",
        "\n",
        "In the computational basis {|00⟩,|01⟩,|10⟩,|11⟩}, the CNOT matrix is defined as follows:\n",
        "\n",
        "\\begin{equation}\n",
        "\\mathrm{CNOT} = \\begin{pmatrix}\n",
        "1 & 0 & 0 & 0 \\\\\n",
        "0 & 1 & 0 & 0 \\\\\n",
        "0 & 0 & 0 & 1 \\\\\n",
        "0 & 0 & 1 & 0\n",
        "\\end{pmatrix}\n",
        "\\end{equation}\n",
        "\n",
        "The Controlled-NOT gate $CNOT_{0,1}$ (controlling on the first qubit with the second qubit as the target) has the following action on computational basis states:\n",
        "\n",
        "\\begin{align}\n",
        "CNOT_{0,1} |00⟩ = |00⟩, \\\\\n",
        "CNOT_{0,1}|01⟩ = |01⟩, \\\\\n",
        "CNOT_{0,1}|10⟩ = |11⟩, \\\\\n",
        "CNOT_{0,1} |11⟩ = |10⟩. \\\\\n",
        "\\end{align}\n",
        "\n",
        "***Extra:***\n",
        ".c_if(qc.clbits[1], 1) and .c_if(qc.clbits[0], 1) are classical control bits that specify whether or not the quantum gate should be applied based on the value of a classical bit. In this case, qc.clbits[1] and qc.clbits[0] are classical bits in the QuantumCircuit object qc, and the gate is applied only if the value of the corresponding classical bit is 1."
      ],
      "metadata": {
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      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Note***\n",
        "We can write: [Ref](10.1109/ACCESS.2019.2960592):\n",
        "\\begin{align}\n",
        "CX(\\Psi, \\Phi^+) ⇒ (|\\Phi^+⟩ → |\\Psi \\oplus \\Phi^+⟩)\n",
        "\\end{align}\n",
        "\n",
        "where,\n",
        "\\begin{align}\n",
        "CX = CNOT &= \n",
        "\\begin{pmatrix} \n",
        "1 & 0 & 0 & 0 \\\\ \n",
        "0 & 1 & 0 & 0 \\\\\n",
        "1 & 0 & 0 & 1 \\\\\n",
        "1 & 0 & 1 & 0\\\\\n",
        "\\end{pmatrix} \n",
        "\\end{align}"
      ],
      "metadata": {
        "id": "cCqIHkGcqZfm"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Quantum Key Distribution (QKD)\n",
        "\n",
        "QKD stands for Quantum Key Distribution, which is a cryptographic technique that uses the principles of quantum mechanics to establish a secure key between two parties. The key can then be used for secure communication using symmetric encryption.\n",
        "\n",
        "The basic idea of QKD is to use the properties of quantum particles (usually photons) to create a secure key that cannot be intercepted or copied without detection. In QKD, two parties (usually referred to as Ram and Shyam) exchange quantum bits (qubits) over a communication channel. Since the act of measurement on a quantum system changes its state, any attempt by an eavesdropper (usually referred to as Eve) to intercept the qubits will be detected by Ram and Shyam.\n",
        "\n",
        "QKD protocols typically involve the use of single photons that are sent over the communication channel in a random sequence. The two parties measure the photons using a basis that is randomly selected for each photon. If the same basis is used by both parties, the measurement results will be correlated. These correlated bits are then used to establish a secure key that can be used for encryption.\n",
        "\n",
        "There are different types of QKD protocols, such as the BB84 protocol, which was proposed by Charles Bennett and Gilles Brassard in 1984, and the E91 protocol, which was proposed by Artur Ekert in 1991. QKD has already been implemented in a number of experimental settings, and it is considered a promising technology for secure communication in the future."
      ],
      "metadata": {
        "id": "CTuxHC7BVlMJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Limitations of Quantum teleportation \n",
        "Quantum teleportation is not what you think of it seeinc pop culture ideas of teleportation!!!\n",
        "\n",
        "1. It requires that*** an entangled bell state*** be split between the sending and receiving destinations.\n",
        "2. Because it requires measuring the bell state, each time you want to perform teleportation, you have to **share a new bell state**!\n",
        "3. It is **not instantaneous**: requires classical communication (a phone call or email) between the sender and receiver.\n",
        "4. It is meant for sending **one qubit at a time**, not a whole stuff (or a person!)!"
      ],
      "metadata": {
        "id": "FAvBIgPxi6z-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# End of Lab\n",
        "\n",
        "---\n",
        "\n",
        "© 2023 Sabin Thapa (for contact, email: sabinthapa240@gmail.com), All rights reserved. "
      ],
      "metadata": {
        "id": "FVYwhUjawB0Z"
      }
    }
  ]
}