# IsCP

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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 on "expand" to the right to view the MATLAB source code for this function.