toqito.channel_props.is_quantum_channel

toqito.channel_props.is_quantum_channel(phi, rtol=1e-05, atol=1e-08)[source]

Determine whether the given input is a quantum channel [WatQC18].

A map \(\Phi \in \text{T} \left(\mathcal{X}, \mathcal{Y} \right)\) is a quantum channel for some choice of complex Euclidean spaces \(\mathcal{X}\) and \(\mathcal{Y}\), if it holds that:

  1. \(\Phi\) is completely positive.

  2. \(\Phi\) is trace preserving.

Examples

We can specify the input as a list of Kraus operators. Consider the map \(\Phi\) defined as

\[\Phi(X) = X - U X U^*\]

where

\[\begin{split}U = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ -1 & 1 \end{pmatrix}.\end{split}\]

References

[WatQC18]

Watrous, John. “The Theory of Quantum Information.” Section: “2.2.1 Definitions and basic notions concerning channels”. Cambridge University Press, 2018.

Parameters:

  • phi – The channel provided as either a Choi matrix or a list of Kraus operators.

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

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

Returns:

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