toqito.channel_props.is_unitary

Determines if a channel is unitary.

Module Contents

toqito.channel_props.is_unitary.is_unitary(phi)

Given a quantum channel, determine if it is unitary.

(Section 2.2.1: Definitions and Basic Notions Concerning Channels from [@Watrous_2018_TQI]).

Let (mathcal{X}) be a complex Euclidean space an let (U in U(mathcal{X})) be a unitary operator. Then a unitary channel is defined as:

[

Phi(X) = U X U^*.

]

Examples

The identity channel is one example of a unitary channel:

[

U = begin{pmatrix}

1 & 0 \ 0 & 1

end{pmatrix}.

]

We can verify this as follows:

```python exec=”1” source=”above” import numpy as np from toqito.channel_props import is_unitary

kraus_ops = [[np.identity(2), np.identity(2)]]

print(is_unitary(kraus_ops)) ```

We can also specify the input as a Choi matrix. For instance, consider the Choi matrix corresponding to the (2)-dimensional completely depolarizing channel.

[

Omega = frac{1}{2} begin{pmatrix}

1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1

end{pmatrix}.

]

We may verify that this channel is not a unitary channel.

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

print(is_unitary(depolarizing(2))) ```

Parameters:

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

Returns:

True if the channel is a unitary channel, and False otherwise.

Return type:

bool