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   "source": [
    "## Ejercicio 4.1: Medida de la polarización de un fotón"
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    "$\\newcommand{\\ket}[1]{|{#1}\\rangle}\\newcommand{\\bra}[1]{\\langle{#1}|}\\DeclareMathOperator{\\Tr}{Tr}$Considere un proceso de medida de la polarización de un fotón\n",
    "\\begin{align*}\n",
    "\\rho = \\ket{\\pi/4}\\bra{\\pi/4}, \\text{ donde }\n",
    "\\ket{\\theta} = \\biggl[\\begin{matrix}\\cos(\\theta)\\\\ \\sin(\\theta)\\end{matrix}\\biggr].\n",
    "\\end{align*}\n",
    "con respecto al POVM $\\bigl\\{\\Pi_{\\leftrightarrow}, \\Pi_{\\updownarrow}\\bigr\\}$.\n",
    "\n",
    "Defina a continuación la matriz de densidad de probabilidad $\\rho$:\n"
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    "\n",
    "\n"
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   "source": [
    "1. Obtenga las probabilidades de observar $\\leftrightarrow$ y $\\updownarrow$ en este proceso de medida."
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   "source": [
    "\n",
    "\n"
   ]
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   "source": [
    "2. Obtenga el nuevo estado $\\rho'$ si se realiza la medida $\\{\\leftrightarrow, \\updownarrow\\}$, pero no se observa su resultado."
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   "source": [
    "\n",
    "\n"
   ]
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   "source": [
    "3. Compare el nuevo estado $\\rho'$ con el correspondiente estado original $\\rho$ y explique el resultado."
   ]
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   "execution_count": null,
   "id": "022dc22a",
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   "outputs": [],
   "source": [
    "\n",
    "\n"
   ]
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