update

Author: mhjensen

doc/pub/week4/html/week4-bs.html

@@ -587,7 +587,7 @@ <h2 id="different-dimensionalities" class="anchor">Different dimensionalities </
 decomposition of a state, we can immmediately say whether it is
 entangled or not. If a state \( \psi \) has is entangled, then its Schmidt
 decomposition has more than one term. Stated differently, the state is
-entangled if the so-called Schmidt rank is is greater than one.  There
+entangled if the so-called Schmidt rank is  greater than one.  There
 is another important property of the Schmidt decomposition which is
 related to the properties of the density matrices and their trace
 operations and the entropies. In order to introduce these concepts we will look
@@ -1011,23 +1011,18 @@ <h2 id="two-qubit-gates" class="anchor">Two-Qubit Gates </h2>
 <!-- !split -->
 <h2 id="control-qubit" class="anchor">Control qubit </h2>
 <p>The control qubit is not acted
-upon. This can be represented as follows:
+upon. This can be represented as follows if
 </p>
-
 $$CU\vert xy\rangle=
-\vert xy\rangle \hspace{0.1cm} \mathrm{if} \hspace{0.1cm}  \vert x \rangle =\vert 0\rangle
-$$
-
-<p>and</p>
-$$
-\vert x \rangle U\vert y \rangle \hspace{0.1cm}  \mathrm{if} \hspace{0.1cm} \vert x \rangle =\vert 1\rangle
+\vert xy\rangle \hspace{0.1cm} \mathrm{if} \hspace{0.1cm}  \vert x \rangle =\vert 0\rangle.
 $$
 
 
 <!-- !split -->
 <h2 id="in-matrix-form" class="anchor">In matrix form </h2>
 
-<p>It can be written in matrix form by writing it as a superposition of
+<p>It is easier to see in a matrix form.
+It can be written in matrix form by writing it as a superposition of
 the two possible cases, each written as a simple tensor product
 </p>
 

doc/pub/week4/html/week4-reveal.html

@@ -617,7 +617,7 @@ <h2 id="different-dimensionalities">Different dimensionalities </h2>
 decomposition of a state, we can immmediately say whether it is
 entangled or not. If a state \( \psi \) has is entangled, then its Schmidt
 decomposition has more than one term. Stated differently, the state is
-entangled if the so-called Schmidt rank is is greater than one.  There
+entangled if the so-called Schmidt rank is  greater than one.  There
 is another important property of the Schmidt decomposition which is
 related to the properties of the density matrices and their trace
 operations and the entropies. In order to introduce these concepts we will look
@@ -1101,27 +1101,20 @@ <h2 id="two-qubit-gates">Two-Qubit Gates </h2>
 <section>
 <h2 id="control-qubit">Control qubit </h2>
 <p>The control qubit is not acted
-upon. This can be represented as follows:
+upon. This can be represented as follows if
 </p>
-
 <p>&nbsp;<br>
 $$CU\vert xy\rangle=
-\vert xy\rangle \hspace{0.1cm} \mathrm{if} \hspace{0.1cm}  \vert x \rangle =\vert 0\rangle
-$$
-<p>&nbsp;<br>
-
-<p>and</p>
-<p>&nbsp;<br>
-$$
-\vert x \rangle U\vert y \rangle \hspace{0.1cm}  \mathrm{if} \hspace{0.1cm} \vert x \rangle =\vert 1\rangle
+\vert xy\rangle \hspace{0.1cm} \mathrm{if} \hspace{0.1cm}  \vert x \rangle =\vert 0\rangle.
 $$
 <p>&nbsp;<br>
 </section>
 
 <section>
 <h2 id="in-matrix-form">In matrix form </h2>
 
-<p>It can be written in matrix form by writing it as a superposition of
+<p>It is easier to see in a matrix form.
+It can be written in matrix form by writing it as a superposition of
 the two possible cases, each written as a simple tensor product
 </p>
 

doc/pub/week4/html/week4-solarized.html

@@ -543,7 +543,7 @@ <h2 id="different-dimensionalities">Different dimensionalities </h2>
 decomposition of a state, we can immmediately say whether it is
 entangled or not. If a state \( \psi \) has is entangled, then its Schmidt
 decomposition has more than one term. Stated differently, the state is
-entangled if the so-called Schmidt rank is is greater than one.  There
+entangled if the so-called Schmidt rank is  greater than one.  There
 is another important property of the Schmidt decomposition which is
 related to the properties of the density matrices and their trace
 operations and the entropies. In order to introduce these concepts we will look
@@ -967,23 +967,18 @@ <h2 id="two-qubit-gates">Two-Qubit Gates </h2>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="control-qubit">Control qubit </h2>
 <p>The control qubit is not acted
-upon. This can be represented as follows:
+upon. This can be represented as follows if
 </p>
-
 $$CU\vert xy\rangle=
-\vert xy\rangle \hspace{0.1cm} \mathrm{if} \hspace{0.1cm}  \vert x \rangle =\vert 0\rangle
-$$
-
-<p>and</p>
-$$
-\vert x \rangle U\vert y \rangle \hspace{0.1cm}  \mathrm{if} \hspace{0.1cm} \vert x \rangle =\vert 1\rangle
+\vert xy\rangle \hspace{0.1cm} \mathrm{if} \hspace{0.1cm}  \vert x \rangle =\vert 0\rangle.
 $$
 
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="in-matrix-form">In matrix form </h2>
 
-<p>It can be written in matrix form by writing it as a superposition of
+<p>It is easier to see in a matrix form.
+It can be written in matrix form by writing it as a superposition of
 the two possible cases, each written as a simple tensor product
 </p>
 

doc/pub/week4/html/week4.html

@@ -620,7 +620,7 @@ <h2 id="different-dimensionalities">Different dimensionalities </h2>
 decomposition of a state, we can immmediately say whether it is
 entangled or not. If a state \( \psi \) has is entangled, then its Schmidt
 decomposition has more than one term. Stated differently, the state is
-entangled if the so-called Schmidt rank is is greater than one.  There
+entangled if the so-called Schmidt rank is  greater than one.  There
 is another important property of the Schmidt decomposition which is
 related to the properties of the density matrices and their trace
 operations and the entropies. In order to introduce these concepts we will look
@@ -1044,23 +1044,18 @@ <h2 id="two-qubit-gates">Two-Qubit Gates </h2>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="control-qubit">Control qubit </h2>
 <p>The control qubit is not acted
-upon. This can be represented as follows:
+upon. This can be represented as follows if
 </p>
-
 $$CU\vert xy\rangle=
-\vert xy\rangle \hspace{0.1cm} \mathrm{if} \hspace{0.1cm}  \vert x \rangle =\vert 0\rangle
-$$
-
-<p>and</p>
-$$
-\vert x \rangle U\vert y \rangle \hspace{0.1cm}  \mathrm{if} \hspace{0.1cm} \vert x \rangle =\vert 1\rangle
+\vert xy\rangle \hspace{0.1cm} \mathrm{if} \hspace{0.1cm}  \vert x \rangle =\vert 0\rangle.
 $$
 
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="in-matrix-form">In matrix form </h2>
 
-<p>It can be written in matrix form by writing it as a superposition of
+<p>It is easier to see in a matrix form.
+It can be written in matrix form by writing it as a superposition of
 the two possible cases, each written as a simple tensor product
 </p>