Update entanglement.ipynb

community/basic_examples/entanglement/entanglement.ipynb

@@ -6,7 +6,7 @@
    "source": [
     "# Quantum Entanglement with Classiq\n",
     "\n",
-    "Entanglement is an important aspect to study the quantum algorithms. In this tutorial, we show how to create a bell pair state $|\\Phi^{+}\\rangle$ of 2 qubits, using the Hadamard and Controlled-NOT transformation."
+    "Entanglement is an important aspect to study the quantum algorithms. In this tutorial, we show how to create a bell pair state $|\\Phi^{+}\\rangle$ of 2 qubits, using the Hadamard and the Controlled-NOT transformation."
    ]
   },
   {
@@ -74,11 +74,11 @@
     "$$\\begin{pmatrix} 1 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0 \\\\ 0 & 0 & 0 & 1 \\\\ 0 & 0 & 1 & 0 \\end{pmatrix} \\begin{pmatrix} \\frac{1}{\\sqrt{2}} \\\\ 0 \\\\ \\frac{1}{\\sqrt{2}}\\\\ 0 \\end{pmatrix} = \\begin{pmatrix} \\frac{1}{\\sqrt{2}} \\\\ 0 \\\\ 0 \\\\ \\frac{1}{\\sqrt{2}} \\end{pmatrix} = \\frac{1}{\\sqrt{2}} \\left| 00 \\right\\rangle + \\frac{1}{\\sqrt{2}} \\left| 11 \\right\\rangle$$\n",
     "\n",
     "In this situation the qubit's of Alice and Bob are correlated to each other.<br>\n",
-    "If we measure the both the qubits we will either get the state $|00\\rangle$ or the state $|11\\rangle$ with equal probability.\n",
+    "If we measure both the qubits we will either get the state $|00\\rangle$ or the state $|11\\rangle$ with equal probability.\n",
     "\n",
     "It is described as:\n",
-    "- When the Alice oberseve her state as $|0\\rangle$ then the state of Bob's qubit collapses to the state $|0\\rangle$\n",
-    "- When the Alice oberseve her state as $|1\\rangle$ then the state of Bob's qubit collapses to the state $|1\\rangle$ \n",
+    "- When Alice oberseve her state as $|0\\rangle$ then the state of Bob's qubit collapses to the state $|0\\rangle$\n",
+    "- When Alice oberseve her state as $|1\\rangle$ then the state of Bob's qubit collapses to the state $|1\\rangle$ \n",
     "\n",
     "The resultant entangled state is designated as a bell pair state $|\\Phi^{+}\\rangle$\n",
     "$$|\\Phi^{+}\\rangle = \\frac{1}{\\sqrt{2}} \\left( |00\\rangle + |11\\rangle \\right)$$\n",