Nathaniel at 15:31, 29 September 2014

2014-09-29T15:31:58Z

← Older revision		Revision as of 15:31, 29 September 2014
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	\|name=PartialMap		\|name=PartialMap
	\|desc=Applies a [[superoperator]] to a subsystem of an operator		\|desc=Applies a [[superoperator]] to a subsystem of an operator
	\|~~req~~=[[ApplyMap]]<br />[[~~iden~~]]<br />[[~~MaxEntangled]]<br />[[opt_args]]<br />[[PermuteSystems~~]]		\|rel=[[ApplyMap]]<br />[[PartialTrace]]<br />[[PartialTranspose]]
	\|~~rel~~=[[~~PartialTrace]]<br />[[PartialTranspose~~]]		\|cat=[[List of functions#Superoperators\|Superoperators]]
	\|upd=January 2, 2013		\|upd=January 2, 2013
	\|v=1.00}}		\|v=0.50}}
	<tt>'''PartialMap'''</tt> is a [[List of functions\|function]] that applies a [[superoperator]] to a subsystem of an operator. Both the superoperator and the operator may be either full or sparse.		<tt>'''PartialMap'''</tt> is a [[List of functions\|function]] that applies a [[superoperator]] to a subsystem of an operator. Both the superoperator and the operator may be either full or sparse.

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	===A random example===		===A random example===
	The following code applies the [[completely depolarizing channel]] to the second subsystem of a random density matrix:		The following code applies the [[completely depolarizing channel]] to the second subsystem of a random density matrix:
	<~~pre<noinclude></noinclude>~~>		<syntaxhighlight>
	>> rho = ~~[[RandomDensityMatrix\|~~RandomDensityMatrix(4)]]		>> rho = RandomDensityMatrix(4)

	rho =		rho =
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	-0.0642 - 0.0250i 0 0.2946 0		-0.0642 - 0.0250i 0 0.2946 0
	0 -0.0642 - 0.0250i 0 0.2946		0 -0.0642 - 0.0250i 0 0.2946
	</~~pre<noinclude></noinclude>~~>		</syntaxhighlight>

	And the following code instead applies the same map to the first subsystem:		And the following code instead applies the same map to the first subsystem:
	<~~pre~~>		<syntaxhighlight>
	>> PartialMap(rho,Phi,1)		>> PartialMap(rho,Phi,1)

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	0 0 0.2231 0.0191 - 0.0079i		0 0 0.2231 0.0191 - 0.0079i
	0 0 0.0191 + 0.0079i 0.2769		0 0 0.0191 + 0.0079i 0.2769
	</~~pre~~>		</syntaxhighlight>

			{{SourceCode\|name=PartialMap}}

Nathaniel: Created page with "{{Function |name=PartialMap |desc=Applies a superoperator to a subsystem of an operator |req=ApplyMap
iden
MaxEntangled
opt_args
[[Perm..."

2013-01-02T18:19:59Z

Created page with "{{Function |name=PartialMap |desc=Applies a superoperator to a subsystem of an operator |req=ApplyMap iden MaxEntangled opt_args [[Perm..."

New page

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

==Syntax==
* <tt>PHIX = PartialMap(X,PHI)</tt>
* <tt>PHIX = PartialMap(X,PHI,SYS)</tt>
* <tt>PHIX = PartialMap(X,PHI,SYS,DIM)</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).
* <tt>SYS</tt> (optional, default 2): The subsystem that the superoperator will be applied to.
* <tt>DIM</tt> (optional, default has <tt>X</tt> acting on two subsystems of equal dimension): A vector containing the dimensions of the (possibly more than 2) subsystems on which <tt>X</tt> acts.

==Examples==
===A random example===
The following code applies the [[completely depolarizing channel]] to the second subsystem of a random density matrix:
<pre<noinclude></noinclude>>
>> rho = [[RandomDensityMatrix|RandomDensityMatrix(4)]]

rho =

0.3101 -0.0220 - 0.0219i -0.0671 - 0.0030i -0.0170 - 0.0694i
-0.0220 + 0.0219i 0.1008 -0.0775 + 0.0492i -0.0613 + 0.0529i
-0.0671 + 0.0030i -0.0775 - 0.0492i 0.1361 0.0602 + 0.0062i
-0.0170 + 0.0694i -0.0613 - 0.0529i 0.0602 - 0.0062i 0.4530

>> Phi = {[1 0;0 0]/sqrt(2);[0 1;0 0]/sqrt(2);[0 0;1 0]/sqrt(2);[0 0;0 1]/sqrt(2)};
>> PartialMap(rho,Phi)

ans =

0.2054 0 -0.0642 + 0.0250i 0
0 0.2054 0 -0.0642 + 0.0250i
-0.0642 - 0.0250i 0 0.2946 0
0 -0.0642 - 0.0250i 0 0.2946
</pre<noinclude></noinclude>>

And the following code instead applies the same map to the first subsystem:
<pre>
>> PartialMap(rho,Phi,1)

ans =

0.2231 0.0191 - 0.0079i 0 0
0.0191 + 0.0079i 0.2769 0 0
0 0 0.2231 0.0191 - 0.0079i
0 0 0.0191 + 0.0079i 0.2769
</pre>

PartialMap - Revision history

Nathaniel at 15:31, 29 September 2014

Nathaniel: Created page with "{{Function |name=PartialMap |desc=Applies a superoperator to a subsystem of an operator |req=ApplyMapidenMaxEntangledopt_args[[Perm..."

Nathaniel: Created page with "{{Function |name=PartialMap |desc=Applies a superoperator to a subsystem of an operator |req=ApplyMap
iden
MaxEntangled
opt_args
[[Perm..."