{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8989e2ba",
   "metadata": {},
   "source": [
    "## Ejemplo 3.1: Modelo de un fotón polarizado"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86c680f2",
   "metadata": {},
   "source": [
    "$\\newcommand{\\ket}[1]{|{#1}\\rangle}\\newcommand{\\bra}[1]{\\langle{#1}|}$El modelo de un fotón polarizado linealmente con un ángulo $\\theta$ se corresponde con un cúbit ya que para  $\\alpha=\\cos(\\theta)$ y $\\beta=\\sin(\\theta)$, se tiene que\n",
    "\\begin{align*}\n",
    "\\ket{\\psi} &= \\cos(\\theta) \\ket{0}  + \\sin(\\theta) \\ket{1}\n",
    "= \\begin{bmatrix}\\cos(\\theta)\\\\ \\sin(\\theta)\\end{bmatrix}.\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8a436d5a",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ket_psi =\n",
      "\n",
      "   0.9211\n",
      "   0.3894\n",
      "\n"
     ]
    }
   ],
   "source": [
    "% Base del espacio de estados cuanticos binarios\n",
    "ket0 = [1; 0];\n",
    "ket1 = [0; 1];\n",
    "\n",
    "% Modelo para un fotón con polarización lineal theta\n",
    "theta = 0.4;\n",
    "ket_psi = cos(theta)*ket0 + sin(theta)*ket1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "118fa2f3",
   "metadata": {},
   "source": [
    "Así, un fotón polarizado se puede interpretar como un vector con corrdenadas $\\cos(\\theta)$ y $\\sin(\\theta)$ en una base formada por los estados ortogonales $\\ket{0}$ y $\\ket{1}$, tal y como representamos en la siguiente figura:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e9cc4b3e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "% Representamos la circunferencia unidad como referencia:\n",
    "set(0, \"defaultaxesfontsize\", 24)  % axes labels\n",
    "t = linspace(0,2*pi,100);\n",
    "plot(cos(t), sin(t), 'k-');\n",
    "\n",
    "% Representamos el estado cuántico ket_psi superpuesto\n",
    "hold on; plot([0;ket_psi(1)], [0;ket_psi(2)], 'k-', 'LineWidth', 2, ...\n",
    "                 ket_psi(1),     ket_psi(2),  'ko', 'LineWidth', 2);\n",
    "axis ([-1.4, 1.4, -1.4, 1.4], \"square\"); grid on;\n",
    "text(ket_psi(1)+.1, ket_psi(2)+.1, '$|\\psi\\rangle$', 'Interpreter', 'Latex');\n",
    "xlabel('$|0\\rangle$', 'Interpreter', 'Latex');\n",
    "ylabel('$|1\\rangle$', 'Interpreter', 'Latex');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6375d947",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
  "kernelspec": {
   "display_name": "Octave",
   "language": "octave",
   "name": "octave"
  },
  "language_info": {
   "file_extension": ".m",
   "help_links": [
    {
     "text": "GNU Octave",
     "url": "https://www.gnu.org/software/octave/support.html"
    },
    {
     "text": "Octave Kernel",
     "url": "https://github.com/Calysto/octave_kernel"
    },
    {
     "text": "MetaKernel Magics",
     "url": "https://metakernel.readthedocs.io/en/latest/source/README.html"
    }
   ],
   "mimetype": "text/x-octave",
   "name": "octave",
   "version": "8.2.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}