ReductionMap

ReductionMap is a function that returns the Choi matrix of the linear map that acts as follows:


 * $$\Phi(X) := \mathrm{Tr}(X)I - X,$$

where $I$ is the identity matrix. This map is positive.

Syntax

 * R = ReductionMap(DIM)
 * R = ReductionMap(DIM,K)

Argument descriptions

 * DIM: The dimension of the reduction map. That is, the size of the matrices that the reduction map acts on.
 * K (optional, default 1): If this positive integer is provided, the script will instead return the Choi matrix of the following linear map:


 * $$\Phi(X) := K\cdot\mathrm{Tr}(X)I - X.$$

The reduction map is positive
The following code returns the Choi matrix of the 3-dimensional reduction map and then verifies that the reduction map is indeed positive (i.e., verifies that its Choi matrix is block positive):

Higher values of K
It is known that the generalization of the reduction map that is provided by the optional argument K is always K-positive, but not (K+1</tt>)-positive. The following code verifies this in the K = 2</tt> case: