IsCP

IsCP
Determines whether or not a superoperator is completely positive
Other toolboxes required	none
Related functions	IsHermPreserving
Function category	Superoperators

IsCP is a function that determines whether or not a given superoperator is completely positive.

Syntax

• CP = IsCP(PHI)
• CP = IsCP(PHI,TOL)

Argument descriptions

• 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).
• TOL (optional, default eps^(3/4)): The numerical tolerance used when determining complete positivity.

Examples

The following code verifies that the map $\Phi$ defined by $\Phi(X) = X - UXU^*$ is not completely positive, where $U = \frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\ -1 & 1\end{bmatrix}$.

>> U = [1 1;-1 1]/sqrt(2);
>> Phi = {eye(2),eye(2); U,-U};
>> IsCP(Phi)

ans =

     0

Source code

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