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   "source": [
    "## Ejemplo 5.2: Estados cuánticos independientes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71cd75b7",
   "metadata": {},
   "source": [
    "$\\newcommand{\\ket}[1]{|{#1}\\rangle}\\newcommand{\\bra}[1]{\\langle{#1}|}$Sean dos estados cuánticos binarios e independientes (que nunca han interaccionado) definidos por las matrices de densidad de probabilidad $\\rho^{A}$ y $\\sigma^{B}$, ambas de dimensión $2\\times 2$. Entonces la matriz de densidad de probabilidad del sistema conjunto es\n",
    "\\begin{align*}\n",
    "        \\delta^{AB} = \\rho^{A} \\otimes \\sigma^{B}.\n",
    "\\end{align*}\n",
    "La dimensión de $\\delta^{AB}$ coincidirá con el producto de las dimensiones de $\\rho^{A}$ y de $\\sigma^{B}$,\n",
    "y será por tanto una matriz cuadrada de dimensión $4 \\times 4$. A partir de los superíndices se puede identificar facilmente si el estado cuántico se corresponde al subsistema $A$, al subsistema $B$ o si está compartido entre ambos."
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     "text": [
      "rhoA =\n",
      "\n",
      "   0.5000   0.5000\n",
      "   0.5000   0.5000\n",
      "\n",
      "sigmaB =\n",
      "\n",
      "   0.2500        0\n",
      "        0   0.7500\n",
      "\n",
      "deltaAB =\n",
      "\n",
      "   0.1250        0   0.1250        0\n",
      "        0   0.3750        0   0.3750\n",
      "   0.1250        0   0.1250        0\n",
      "        0   0.3750        0   0.3750\n",
      "\n"
     ]
    }
   ],
   "source": [
    "rhoA   = [[1/2, 1/2]; [1/2, 1/2]]\n",
    "sigmaB = [[1/4, 0]; [0, 3/4]]\n",
    "deltaAB = kron(rhoA, sigmaB)"
   ]
  }
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