Wording

src/fundamentals/main.tex

@@ -84,7 +84,7 @@ as a vector}
 The so called Bra-ket or Dirac notation is especially appropriate,
 having been proposed by Paul Dirac in 1939 for the express purpose
 of simplifying quantum mechanical notation \cite{dirac_new_1939}.
-Two new symbols are introduced, \emph{bra}s $\bra{\cdot}$ and
+Two new symbols are defined, \emph{bra}s $\bra{\cdot}$ and
 \emph{ket}s $\ket{\cdot}$.
 Kets denote ordinary vectors, while bras denote their Hermitian conjugates.
 For example, two vectors specified by the labels $a$ and $b$
@@ -119,7 +119,8 @@ Their inner product is $\braket{a\vert b}$.
         .%
     \end{align*}%
     %
-    \ldots When not ambiguous in the context, the tensor product symbol may be omitted, e.g.
+    \ldots When not ambiguous in the context, the tensor product
+    symbol may be omitted, e.g.,
     \begin{align*}
         \ket{0} \otimes \ket{0} = \ket{0}\ket{0}
         .%
@@ -128,7 +129,7 @@ Their inner product is $\braket{a\vert b}$.
 
 As we will see, the core concept that gives quantum computing its
 power is entanglement. When two quantum mechanical systems are
-entangled, measuring the state of one will collapse the state of the other.
+entangled, measuring the state of one will collapse that of the other.
 Take for example two subsystems with the overall state
 %
 \begin{align*}
@@ -137,9 +138,9 @@ Take for example two subsystems with the overall state
     .%
 \end{align*}
 %
-If we measure the state of the first subsystem as $\ket{0}$, we can
+If we measure the first subsystem as being in $\ket{0}$, we can
 be certain that a measurement of the second subsystem will also yield $\ket{0}$.
-For brevity, we write the state of the combined system as%
+Introducing a new notation for entangled states, we can write%
 %
 \begin{align*}
     \ket{\psi} = \frac{1}{\sqrt{2}} \left( \ket{00} + \ket{11} \right)