Difference between revisions of "PartialMap"
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(Created page with "{{Function |name=PartialMap |desc=Applies a superoperator to a subsystem of an operator |req=ApplyMap<br />iden<br />MaxEntangled<br />opt_args<br />[[Perm...") |
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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 | ||
| − | | | + | |rel=[[ApplyMap]]<br />[[PartialTrace]]<br />[[PartialTranspose]] |
| − | | | + | |cat=[[List of functions#Superoperators|Superoperators]] |
|upd=January 2, 2013 | |upd=January 2, 2013 | ||
| − | |v= | + | |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: | ||
| − | < | + | <syntaxhighlight> |
| − | >> rho = | + | >> 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 | ||
| − | </ | + | </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: | ||
| − | < | + | <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 | ||
| − | </ | + | </syntaxhighlight> |
| + | |||
| + | {{SourceCode|name=PartialMap}} | ||
Latest revision as of 15:31, 29 September 2014
| PartialMap | |
| Applies a superoperator to a subsystem of an operator | |
| Other toolboxes required | none |
|---|---|
| Related functions | ApplyMap PartialTrace PartialTranspose |
| Function category | Superoperators |
PartialMap is a function that applies a superoperator to a subsystem of an operator. Both the superoperator and the operator may be either full or sparse.
Syntax
- PHIX = PartialMap(X,PHI)
- PHIX = PartialMap(X,PHI,SYS)
- PHIX = PartialMap(X,PHI,SYS,DIM)
Argument descriptions
- X: A matrix.
- PHI: 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).
- SYS (optional, default 2): The subsystem that the superoperator will be applied to.
- DIM (optional, default has X acting on two subsystems of equal dimension): A vector containing the dimensions of the (possibly more than 2) subsystems on which X acts.
Examples
A random example
The following code applies the completely depolarizing channel to the second subsystem of a random density matrix:
>> rho = 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 0.2946And the following code instead applies the same map to the first subsystem:
>> 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 0.2769Source code
Click here to view this function's source code on github.