toqito.channels.reduction

Generates the reduction channel.

Module Contents

toqito.channels.reduction.reduction(dim, k=1)

Produce the reduction map or reduction channel [@WikiReductionCrit].

If k = 1, this returns the Choi matrix of the reduction map which is a positive map on dim-by-dim matrices. For a different value of k, this yields the Choi matrix of the map defined by:

[

R(X) = k * text{Tr}(X) * mathbb{I} - X,

]

where (mathbb{I}) is the identity matrix. This map is (k)-positive.

Examples

Using |toqito⟩, we can generate the (3)-dimensional (or standard) reduction map as follows.

```python exec=”1” source=”above” from toqito.channels import reduction

print(reduction(3)) ```

Parameters:

• dim (int) – A positive integer (the dimension of the reduction map).

• k (int) – If this positive integer is provided, the script will instead return the Choi matrix of the following

• map (linear) – Phi(X) := K * Tr(X)I - X.

Returns:

The reduction map.

Return type:

numpy.ndarray