toqito.channel_props.is_unital

Determines if a channel is unital.

Module Contents

toqito.channel_props.is_unital.is_unital(phi, rtol=1e-05, atol=1e-08, dim=None)

Determine whether the given channel is unital.

A map (Phi in text{T} left(mathcal{X}, mathcal{Y} right)) is unital if it holds that:

[

Phi(mathbb{I}_{mathcal{X}}) = mathbb{I}_{mathcal{Y}}.

]

If the input channel maps (M_{r,c}) to (M_{x,y}) then dim should be the list [[r,x], [c,y]]. If it maps (M_m) to (M_n), then dim can simply be the vector [m,n].

More information can be found in Chapter: Unital Channels And Majorization from [@Watrous_2018_TQI]).

Examples

Consider the channel whose Choi matrix is the swap operator. This channel is an example of a unital channel.

```python exec=”1” source=”above” from toqito.perms import swap_operator from toqito.channel_props import is_unital

choi = swap_operator(3)

print(is_unital(choi)) ```

Additionally, the channel whose Choi matrix is the depolarizing channel is another example of a unital channel.

```python exec=”1” source=”above” from toqito.channels import depolarizing from toqito.channel_props import is_unital

choi = depolarizing(4)

print(is_unital(choi)) ```

Parameters:

• phi (numpy.ndarray | list[list[numpy.ndarray]]) – The channel provided as either a Choi matrix or a list of Kraus operators.

• rtol (float) – The relative tolerance parameter (default 1e-05).

• atol (float) – The absolute tolerance parameter (default 1e-08).

• dim (int | list[int] | numpy.ndarray | None) – A scalar, vector or matrix containing the input and output dimensions of PHI.

Returns:

True if the channel is unital, and False otherwise.

Return type:

bool