PartialMap

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             0.2946

And 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   0.2769

Source code

Click here to view this function's source code on github.