ApplyMap - Revision history

Nathaniel at 17:58, 12 November 2014

2014-11-12T17:58:14Z

Nathaniel at 15:20, 29 September 2014

2014-09-29T15:20:06Z

Nathaniel: Created page with "{{Function |name=ApplyMap |desc=Applies a superoperator to an operator |rel=PartialMap |upd=January 2, 2013 |v=1.00}} `'''ApplyMap'''` is a [[List of functions|..."

2013-01-02T17:10:02Z

Created page with "{{Function |name=ApplyMap |desc=Applies a superoperator to an operator |rel=PartialMap |upd=January 2, 2013 |v=1.00}} <tt>'''ApplyMap'''</tt> is a [[List of functions|..."

New page

{{Function
|name=ApplyMap
|desc=Applies a [[superoperator]] to an operator
|rel=[[PartialMap]]
|upd=January 2, 2013
|v=1.00}}
<tt>'''ApplyMap'''</tt> is a [[List of functions|function]] that applies a [[superoperator]] to an operator. Both the superoperator and the operator may be either full or sparse.

==Syntax==
* <tt>PHIX = ApplyMap(X,PHI)</tt>

==Argument descriptions==
* <tt>X</tt>: A matrix.
* <tt>PHI</tt>: A superoperator. Should be provided as either a [[Choi matrix]], or as a cell with either 1 or 2 columns (see the [[tutorial]] page for more details about specifying superoperators within QETLAB).

==Examples==
===A random example===
The following code computes $\Phi(X)$, where $X = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}$ and $\Phi$ is the superoperator defined by
$$
\Phi(X) = \begin{bmatrix}1 & 5 \\ 1 & 0 \\ 0 & 2\end{bmatrix}X\begin{bmatrix}0 & 1 \\ 2 & 3 \\ 4 & 5\end{bmatrix}^\dagger - \begin{bmatrix}1 & 0 \\ 0 & 0 \\ 0 & 1\end{bmatrix}X\begin{bmatrix}0 & 0 \\ 1 & 1 \\ 0 & 0\end{bmatrix}^\dagger.
$$
<pre>
>> X = [1 2;3 4];
>> Phi = {[1 5;1 0;0 2] [0 1;2 3;4 5];[-1 0;0 0;0 -1] [0 0;1 1;0 0]};
>> ApplyMap(X,Phi)

ans =

22 95 174
2 8 14
8 29 64
</pre>

===Transpose map===
The [[swap operator]] is the Choi matrix of the [[transpose]] map. Thus, the following code is a (rather slow and ugly) way of computing the transpose of a matrix:
<pre<noinclude></noinclude>>
>> X = reshape(1:9,3,3)

X =

1 4 7
2 5 8
3 6 9

>> ApplyMap(X,[[SwapOperator|SwapOperator(3)]])

ans =

1 2 3
4 5 6
7 8 9
</pre<noinclude></noinclude>>

Of course, in practice you should just use MATLAB's built-in transposition operator <tt>X.'</tt>.

@@ Line 4: / Line 4: @@
 |rel=[[PartialMap]]
 |cat=[[List of functions#Superoperators|Superoperators]]
-|upd=January 2, 2013
+|upd=November 12, 2014
 |v=0.50}}
 <tt>'''ApplyMap'''</tt> is a [[List of functions|function]] that applies a [[superoperator]] to an operator. Both the superoperator and the operator may be either full or sparse.

@@ Line 3: / Line 3: @@
 |desc=Applies a [[superoperator]] to an operator
 |rel=[[PartialMap]]
 |upd=January 2, 2013
-|v=1.00}}
+|v=0.50}}
 <tt>'''ApplyMap'''</tt> is a [[List of functions|function]] that applies a [[superoperator]] to an operator. Both the superoperator and the operator may be either full or sparse.
@@ Line 20: / Line 21: @@
    \Phi(X) = \begin{bmatrix}1 & 5 \\ 1 & 0 \\ 0 & 2\end{bmatrix}X\begin{bmatrix}0 & 1 \\ 2 & 3 \\ 4 & 5\end{bmatrix}^\dagger - \begin{bmatrix}1 & 0 \\ 0 & 0 \\ 0 & 1\end{bmatrix}X\begin{bmatrix}0 & 0 \\ 1 & 1 \\ 0 & 0\end{bmatrix}^\dagger.
 $$
-<pre>
+<syntaxhighlight>
 >> X = [1 2;3 4];
 >> Phi = {[1 5;1 0;0 2] [0 1;2 3;4 5];[-1 0;0 0;0 -1] [0 0;1 1;0 0]};
@@ Line 30: / Line 31: @@
      8    14
     29    64
-</pre>
+</syntaxhighlight>
 ===Transpose map===
 The [[swap operator]] is the Choi matrix of the [[transpose]] map. Thus, the following code is a (rather slow and ugly) way of computing the transpose of a matrix:
-<pre<noinclude></noinclude>>
+<syntaxhighlight>
 >> X = reshape(1:9,3,3)
@@ Line 43: / Line 44: @@
      6     9
->> ApplyMap(X,[[SwapOperator|SwapOperator(3)]])
+>> ApplyMap(X,SwapOperator(3))
 ans =
@@ Line 50: / Line 51: @@
      5     6
      8     9
-</pre<noinclude></noinclude>>
+</syntaxhighlight>
 Of course, in practice you should just use MATLAB's built-in transposition operator <tt>X.'</tt>.

ApplyMap - Revision history

Nathaniel at 17:58, 12 November 2014

Nathaniel at 15:20, 29 September 2014

Nathaniel: Created page with "{{Function |name=ApplyMap |desc=Applies a superoperator to an operator |rel=PartialMap |upd=January 2, 2013 |v=1.00}} '''ApplyMap''' is a [[List of functions|..."

Nathaniel: Created page with "{{Function |name=ApplyMap |desc=Applies a superoperator to an operator |rel=PartialMap |upd=January 2, 2013 |v=1.00}} `'''ApplyMap'''` is a [[List of functions|..."