update

Author: mhjensen

doc/pub/week2/html/week2-bs.html

@@ -48,7 +48,6 @@
                2,
                None,
                'properties-of-a-measurement'),
-              ('Entanglement', 2, None, 'entanglement'),
               ('Basic properties of hermitian operators',
                2,
                None,
@@ -175,7 +174,6 @@
      <!-- navigation toc: --> <li><a href="#new-zoom-link" style="font-size: 80%;">New zoom link</a></li>
      <!-- navigation toc: --> <li><a href="#measurements" style="font-size: 80%;">Measurements</a></li>
      <!-- navigation toc: --> <li><a href="#properties-of-a-measurement" style="font-size: 80%;">Properties of a measurement</a></li>
-     <!-- navigation toc: --> <li><a href="#entanglement" style="font-size: 80%;">Entanglement</a></li>
      <!-- navigation toc: --> <li><a href="#basic-properties-of-hermitian-operators" style="font-size: 80%;">Basic properties of hermitian operators</a></li>
      <!-- navigation toc: --> <li><a href="#the-pauli-matrices-again" style="font-size: 80%;">The Pauli matrices again</a></li>
      <!-- navigation toc: --> <li><a href="#spectral-decomposition" style="font-size: 80%;">Spectral Decomposition</a></li>
@@ -341,28 +339,14 @@ <h2 id="properties-of-a-measurement" class="anchor">Properties of a measurement
 us now look at other types of operations we can make on qubit states.
 </p>
 
-<!-- !split -->
-<h2 id="entanglement" class="anchor">Entanglement  </h2>
-
-<p>In order to study entanglement and why it is so important for quantum
-computing, we need to introduce some basic measures and useful
-quantities.  These quantities are the spectral decomposition of
-hermitian operators, how these are then used to define measurements
-and how we can define so-called density operators (matrices). These
-are all quantities which will become very useful when we discuss
-entanglement and in particular how to quantify it. In order to define
-these quantities we need first to remind ourselves about some basic linear
-algebra properties of hermitian operators and matrices.
-</p>
-
 <!-- !split -->
 <h2 id="basic-properties-of-hermitian-operators" class="anchor">Basic properties of hermitian operators </h2>
 
 <p>The operators we typically encounter in quantum mechanical studies are</p>
 <ol>
 <li> Hermitian (self-adjoint) meaning that for example the elements of a Hermitian matrix \( \boldsymbol{U} \) obey \( u_{ij}=u_{ji}^* \).</li>
 <li> Unitary \( \boldsymbol{U}\boldsymbol{U}^{\dagger}=\boldsymbol{U}^{\dagger}\boldsymbol{U}=\boldsymbol{I} \), where \( \boldsymbol{I} \) is the unit matrix</li>
-<li> The oparator \( \boldsymbol{U} \) and its self-adjoint commute (often labeled as normal operators), that is  \( [\boldsymbol{U},\boldsymbol{U}^{\dagger}]=0 \). An operator is <b>normal</b> if and only if it is diagonalizable. A Hermitian operator is normal.</li>
+<li> The operator \( \boldsymbol{U} \) and its self-adjoint commute (often labeled as normal operators), that is  \( [\boldsymbol{U},\boldsymbol{U}^{\dagger}]=0 \). An operator is <b>normal</b> if and only if it is diagonalizable. A Hermitian operator is normal.</li>
 </ol>
 <p>Unitary operators in a Hilbert space preserve the norm and orthogonality. If \( \boldsymbol{U} \) is a unitary operator acting on a state \( \vert \psi_j\rangle \), the action of</p>
 
@@ -814,7 +798,7 @@ <h2 id="extending-the-expressions" class="anchor">Extending the expressions </h2
 p(x)=\sum_{i=0}^{n-1}p_i\boldsymbol{P}_{\psi_i(x)},
 $$
 
-<p>where \( p_i \) are the probabilities of a specific outcome.  Add later a digression on marginal probabilities.</p>
+<p>where \( p_i \) are the probabilities of a specific outcome. </p>
 
 <p>With these prerequisites we are now ready to introduce the density  matrices, or density operators.</p>
 

doc/pub/week2/html/week2-reveal.html

@@ -282,29 +282,14 @@ <h2 id="properties-of-a-measurement">Properties of a measurement </h2>
 </p>
 </section>
 
-<section>
-<h2 id="entanglement">Entanglement  </h2>
-
-<p>In order to study entanglement and why it is so important for quantum
-computing, we need to introduce some basic measures and useful
-quantities.  These quantities are the spectral decomposition of
-hermitian operators, how these are then used to define measurements
-and how we can define so-called density operators (matrices). These
-are all quantities which will become very useful when we discuss
-entanglement and in particular how to quantify it. In order to define
-these quantities we need first to remind ourselves about some basic linear
-algebra properties of hermitian operators and matrices.
-</p>
-</section>
-
 <section>
 <h2 id="basic-properties-of-hermitian-operators">Basic properties of hermitian operators </h2>
 
 <p>The operators we typically encounter in quantum mechanical studies are</p>
 <ol>
 <p><li> Hermitian (self-adjoint) meaning that for example the elements of a Hermitian matrix \( \boldsymbol{U} \) obey \( u_{ij}=u_{ji}^* \).</li>
 <p><li> Unitary \( \boldsymbol{U}\boldsymbol{U}^{\dagger}=\boldsymbol{U}^{\dagger}\boldsymbol{U}=\boldsymbol{I} \), where \( \boldsymbol{I} \) is the unit matrix</li>
-<p><li> The oparator \( \boldsymbol{U} \) and its self-adjoint commute (often labeled as normal operators), that is  \( [\boldsymbol{U},\boldsymbol{U}^{\dagger}]=0 \). An operator is <b>normal</b> if and only if it is diagonalizable. A Hermitian operator is normal.</li>
+<p><li> The operator \( \boldsymbol{U} \) and its self-adjoint commute (often labeled as normal operators), that is  \( [\boldsymbol{U},\boldsymbol{U}^{\dagger}]=0 \). An operator is <b>normal</b> if and only if it is diagonalizable. A Hermitian operator is normal.</li>
 </ol>
 <p>
 <p>Unitary operators in a Hilbert space preserve the norm and orthogonality. If \( \boldsymbol{U} \) is a unitary operator acting on a state \( \vert \psi_j\rangle \), the action of</p>
@@ -861,7 +846,7 @@ <h2 id="extending-the-expressions">Extending the expressions </h2>
 $$
 <p>&nbsp;<br>
 
-<p>where \( p_i \) are the probabilities of a specific outcome.  Add later a digression on marginal probabilities.</p>
+<p>where \( p_i \) are the probabilities of a specific outcome. </p>
 
 <p>With these prerequisites we are now ready to introduce the density  matrices, or density operators.</p>
 </section>

doc/pub/week2/html/week2-solarized.html

@@ -75,7 +75,6 @@
                2,
                None,
                'properties-of-a-measurement'),
-              ('Entanglement', 2, None, 'entanglement'),
               ('Basic properties of hermitian operators',
                2,
                None,
@@ -284,28 +283,14 @@ <h2 id="properties-of-a-measurement">Properties of a measurement </h2>
 us now look at other types of operations we can make on qubit states.
 </p>
 
-<!-- !split --><br><br><br><br><br><br><br><br><br><br>
-<h2 id="entanglement">Entanglement  </h2>
-
-<p>In order to study entanglement and why it is so important for quantum
-computing, we need to introduce some basic measures and useful
-quantities.  These quantities are the spectral decomposition of
-hermitian operators, how these are then used to define measurements
-and how we can define so-called density operators (matrices). These
-are all quantities which will become very useful when we discuss
-entanglement and in particular how to quantify it. In order to define
-these quantities we need first to remind ourselves about some basic linear
-algebra properties of hermitian operators and matrices.
-</p>
-
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="basic-properties-of-hermitian-operators">Basic properties of hermitian operators </h2>
 
 <p>The operators we typically encounter in quantum mechanical studies are</p>
 <ol>
 <li> Hermitian (self-adjoint) meaning that for example the elements of a Hermitian matrix \( \boldsymbol{U} \) obey \( u_{ij}=u_{ji}^* \).</li>
 <li> Unitary \( \boldsymbol{U}\boldsymbol{U}^{\dagger}=\boldsymbol{U}^{\dagger}\boldsymbol{U}=\boldsymbol{I} \), where \( \boldsymbol{I} \) is the unit matrix</li>
-<li> The oparator \( \boldsymbol{U} \) and its self-adjoint commute (often labeled as normal operators), that is  \( [\boldsymbol{U},\boldsymbol{U}^{\dagger}]=0 \). An operator is <b>normal</b> if and only if it is diagonalizable. A Hermitian operator is normal.</li>
+<li> The operator \( \boldsymbol{U} \) and its self-adjoint commute (often labeled as normal operators), that is  \( [\boldsymbol{U},\boldsymbol{U}^{\dagger}]=0 \). An operator is <b>normal</b> if and only if it is diagonalizable. A Hermitian operator is normal.</li>
 </ol>
 <p>Unitary operators in a Hilbert space preserve the norm and orthogonality. If \( \boldsymbol{U} \) is a unitary operator acting on a state \( \vert \psi_j\rangle \), the action of</p>
 
@@ -757,7 +742,7 @@ <h2 id="extending-the-expressions">Extending the expressions </h2>
 p(x)=\sum_{i=0}^{n-1}p_i\boldsymbol{P}_{\psi_i(x)},
 $$
 
-<p>where \( p_i \) are the probabilities of a specific outcome.  Add later a digression on marginal probabilities.</p>
+<p>where \( p_i \) are the probabilities of a specific outcome. </p>
 
 <p>With these prerequisites we are now ready to introduce the density  matrices, or density operators.</p>
 

doc/pub/week2/html/week2.html

@@ -152,7 +152,6 @@
                2,
                None,
                'properties-of-a-measurement'),
-              ('Entanglement', 2, None, 'entanglement'),
               ('Basic properties of hermitian operators',
                2,
                None,
@@ -361,28 +360,14 @@ <h2 id="properties-of-a-measurement">Properties of a measurement </h2>
 us now look at other types of operations we can make on qubit states.
 </p>
 
-<!-- !split --><br><br><br><br><br><br><br><br><br><br>
-<h2 id="entanglement">Entanglement  </h2>
-
-<p>In order to study entanglement and why it is so important for quantum
-computing, we need to introduce some basic measures and useful
-quantities.  These quantities are the spectral decomposition of
-hermitian operators, how these are then used to define measurements
-and how we can define so-called density operators (matrices). These
-are all quantities which will become very useful when we discuss
-entanglement and in particular how to quantify it. In order to define
-these quantities we need first to remind ourselves about some basic linear
-algebra properties of hermitian operators and matrices.
-</p>
-
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="basic-properties-of-hermitian-operators">Basic properties of hermitian operators </h2>
 
 <p>The operators we typically encounter in quantum mechanical studies are</p>
 <ol>
 <li> Hermitian (self-adjoint) meaning that for example the elements of a Hermitian matrix \( \boldsymbol{U} \) obey \( u_{ij}=u_{ji}^* \).</li>
 <li> Unitary \( \boldsymbol{U}\boldsymbol{U}^{\dagger}=\boldsymbol{U}^{\dagger}\boldsymbol{U}=\boldsymbol{I} \), where \( \boldsymbol{I} \) is the unit matrix</li>
-<li> The oparator \( \boldsymbol{U} \) and its self-adjoint commute (often labeled as normal operators), that is  \( [\boldsymbol{U},\boldsymbol{U}^{\dagger}]=0 \). An operator is <b>normal</b> if and only if it is diagonalizable. A Hermitian operator is normal.</li>
+<li> The operator \( \boldsymbol{U} \) and its self-adjoint commute (often labeled as normal operators), that is  \( [\boldsymbol{U},\boldsymbol{U}^{\dagger}]=0 \). An operator is <b>normal</b> if and only if it is diagonalizable. A Hermitian operator is normal.</li>
 </ol>
 <p>Unitary operators in a Hilbert space preserve the norm and orthogonality. If \( \boldsymbol{U} \) is a unitary operator acting on a state \( \vert \psi_j\rangle \), the action of</p>
 
@@ -834,7 +819,7 @@ <h2 id="extending-the-expressions">Extending the expressions </h2>
 p(x)=\sum_{i=0}^{n-1}p_i\boldsymbol{P}_{\psi_i(x)},
 $$
 
-<p>where \( p_i \) are the probabilities of a specific outcome.  Add later a digression on marginal probabilities.</p>
+<p>where \( p_i \) are the probabilities of a specific outcome. </p>
 
 <p>With these prerequisites we are now ready to introduce the density  matrices, or density operators.</p>