Merge pull request #39 from GBisi/patch-4

Update 05-entanglement.Rmd

source/05-entanglement.Rmd

@@ -690,7 +690,7 @@ $$
 for *any* $\ket{\psi}$.
 *But this is not true!*
 
-The unitarity of the $\texttt{c-NOT}$ means that it turns *superpositions* in the control qubit into *entanglement* of the control and the target: if the control qubit is in the a superposition state $\ket{\psi} = \alpha\ket{0}+\beta\ket{1}$ (with $\alpha,\beta\neq0$), and the target is in $\ket{0}$, then the $\texttt{c-NOT}$ gate generates the entangled state
+The unitarity of the $\texttt{c-NOT}$ means that it turns *superpositions* in the control qubit into *entanglement* of the control and the target: if the control qubit is in the superposition state $\ket{\psi} = \alpha\ket{0}+\beta\ket{1}$ (with $\alpha,\beta\neq0$), and the target is in $\ket{0}$, then the $\texttt{c-NOT}$ gate generates the entangled state
 $$
   \big( \alpha\ket{0}+\beta\ket{1} \big) \ket{0}
   \xmapsto{\texttt{c-NOT}}
@@ -740,7 +740,7 @@ We won't look at all of them in depth, but it's worth mentioning them here and g
 
   This can be seen as a consequence of no-cloning: if we were able to turn a quantum state into classical information and then back again, we could simply clone the classical information and then get a cloned copy of our quantum state.
 
-  The name it a bit confusing, because we have just seen that *quantum* teleportation is possible through the use of entanglement, but it refers to the idea of *classical* teleportation of quantum states.
+  The name is a bit confusing, because we have just seen that *quantum* teleportation is possible through the use of entanglement, but it refers to the idea of *classical* teleportation of quantum states.
 
   Note that the "converse" to this is possible though: if we start with some *classical* information then we can convert it to quantum information and then back again perfectly fine (for example, using the fact that orthogonal states can be perfectly distinguished).