ChoiMap

ChoiMap
Produces the Choi map or one of its generalizations
Other toolboxes required	iden MaxEntangled opt_args

ChoiMap is a function that returns the Choi matrix of the linear map on $3 \times 3$ matrices that acts as follows:

\[\begin{bmatrix}x_{11} & x_{12} & x_{13} \\ x_{21} & x_{22} & x_{23} \\ x_{31} & x_{32} & x_{33}\end{bmatrix} \mapsto \begin{bmatrix}ax_{11}+bx_{22}+cx_{33} & -x_{12} & -x_{13} \\ -x_{21} & cx_{11}+ax_{22}+bx_{33} & -x_{23} \\ -x_{31} & -x_{32} & bx_{11}+cx_{22}+ax_{33}\end{bmatrix},\]

where $a,b,c$ are given real numbers. This map is positive if and only if $a \geq 1$, $a + b + c \geq 3$, and $bc \geq (2-a)^2$ whenever $1 \leq a \leq 2$.

Syntax

• C = ChoiMap()
• C = ChoiMap(A,B,C)

Argument descriptions

• A,B,C: Real parameters of the Choi map. If they are not provided, the default Choi map (with A = B = 1 and C = 0) is returned.

Examples

The standard Choi map

The following code returns the Choi matrix of the Choi map:

>> ChoiMap()

ans =

     1     0     0     0    -1     0     0     0    -1
     0     0     0     0     0     0     0     0     0
     0     0     1     0     0     0     0     0     0
     0     0     0     1     0     0     0     0     0
    -1     0     0     0     1     0     0     0    -1
     0     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     1     0
    -1     0     0     0    -1     0     0     0     1