DualMap - Revision history

Nathaniel at 02:26, 28 November 2014

2014-11-28T02:26:28Z

Nathaniel at 18:01, 12 November 2014

2014-11-12T18:01:28Z

Nathaniel at 15:27, 29 September 2014

2014-09-29T15:27:51Z

Nathaniel: notation

2013-01-22T17:32:21Z

notation

Nathaniel: Created page with "{{Function |name=DualMap |desc=Computes the dual of a superoperator in the Hilbert-Schmidt inner product |rel=ComplementaryMap |upd=January 21, 2013 |v=1...."

2013-01-21T17:50:54Z

Created page with "{{Function |name=DualMap |desc=Computes the dual of a superoperator in the Hilbert-Schmidt inner product |rel=ComplementaryMap |upd=January 21, 2013 |v=1...."

New page

{{Function
|name=DualMap
|desc=Computes the [[dual map|dual]] of a superoperator in the [[Hilbert-Schmidt inner product]]
|rel=[[ComplementaryMap]]
|upd=January 21, 2013
|v=1.00}}
<tt>'''DualMap'''</tt> is a [[List of functions|function]] that computes the [[dual map|dual]] of a superoperator in the [[Hilbert-Schmidt inner product]]. If $\Phi(X) = \sum_j A_j X B_j^*$ for all matrices $X$, then the dual map is defined by $\Phi^\dagger(Y) = \sum_j A_j^\dagger Y B_j$.

==Syntax==
* <tt>PHID = DualMap(PHI)</tt>
* <tt>PHID = DualMap(PHI,DIM)</tt>

==Argument descriptions==
* <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). <tt>PHID</tt> will be a cell of Kraus operators if <tt>PHI</tt> is a cell of Kraus operators, and similarly <tt>PHID</tt> will be a Choi matrix if <tt>PHI</tt> is a Choi matrix.
* <tt>DIM</tt> (optional, default has input and output spaces of equal dimension): A 1-by-2 vector containing the input and output dimensions of <tt>PHI</tt>, in that order (equivalently, these are the dimensions of the first and second subsystems of the Choi matrix <tt>PHI</tt>, in that order). If the input or output space is not square, then <tt>DIM</tt>'s first row should contain the input and output row dimensions, and its second row should contain its input and output column dimensions. <tt>DIM</tt> is required if and only if <tt>PHI</tt> has unequal input and output dimensions and is provided as a Choi matrix.

==Examples==
To be added.

@@ Line 4: / Line 4: @@
 |rel=[[ComplementaryMap]]
 |cat=[[List of functions#Superoperators|Superoperators]]
-|upd=November 12, 2014
+|upd=November 24, 2014}}
 <tt>'''DualMap'''</tt> is a [[List of functions|function]] that computes the dual of a superoperator in the Hilbert-Schmidt inner product. If $\Phi(X) = \sum_j A_j X B_j^\dagger$ for all matrices $X$, then the dual map is defined by $\Phi^\dagger(Y) = \sum_j A_j^\dagger Y B_j$.

@@ Line 1: / Line 1: @@
 {{Function
 |name=DualMap
-|desc=Computes the [[dual map|dual]] of a superoperator in the [[Hilbert-Schmidt inner product]]
+|desc=Computes the dual of a superoperator in the Hilbert-Schmidt inner product
 |rel=[[ComplementaryMap]]
 |cat=[[List of functions#Superoperators|Superoperators]]
-|upd=January 21, 2013
+|upd=November 12, 2014
 |v=0.50}}
-<tt>'''DualMap'''</tt> is a [[List of functions|function]] that computes the [[dual map|dual]] of a superoperator in the [[Hilbert-Schmidt inner product]]. If $\Phi(X) = \sum_j A_j X B_j^\dagger$ for all matrices $X$, then the dual map is defined by $\Phi^\dagger(Y) = \sum_j A_j^\dagger Y B_j$.
+<tt>'''DualMap'''</tt> is a [[List of functions|function]] that computes the dual of a superoperator in the Hilbert-Schmidt inner product. If $\Phi(X) = \sum_j A_j X B_j^\dagger$ for all matrices $X$, then the dual map is defined by $\Phi^\dagger(Y) = \sum_j A_j^\dagger Y B_j$.
 ==Syntax==

@@ Line 3: / Line 3: @@
 |desc=Computes the [[dual map|dual]] of a superoperator in the [[Hilbert-Schmidt inner product]]
 |rel=[[ComplementaryMap]]
 |upd=January 21, 2013
-|v=1.00}}
+|v=0.50}}
 <tt>'''DualMap'''</tt> is a [[List of functions|function]] that computes the [[dual map|dual]] of a superoperator in the [[Hilbert-Schmidt inner product]]. If $\Phi(X) = \sum_j A_j X B_j^\dagger$ for all matrices $X$, then the dual map is defined by $\Phi^\dagger(Y) = \sum_j A_j^\dagger Y B_j$.
@@ Line 16: / Line 17: @@
 ==Examples==
-To be added.
+===The dual of the dual map===