A quantum channel can be defined as a completely positive and trace preserving linear map.
More formally, let \mathcal{X} and \mathcal{Y} represent complex Euclidean spaces and let \text{L}(\cdot) represent the set of linear operators. Then a quantum channel, \Phi is defined as
\Phi : \text{L}(\mathcal{X}) \rightarrow \text{L}(\mathcal{Y})
such that \Phi is completely positive and trace preserving.
.. toctree::
.. autosummary::
:toctree: _autosummary
toqito.channel_metrics.channel_fidelity
.. toctree::
.. autosummary::
:toctree: _autosummary
toqito.channels.choi
toqito.channels.dephasing
toqito.channels.depolarizing
toqito.channels.partial_trace
toqito.channels.partial_transpose
toqito.channels.realignment
toqito.channels.reduction
.. toctree::
.. autosummary::
:toctree: _autosummary
toqito.channel_ops.apply_channel
toqito.channel_ops.choi_to_kraus
toqito.channel_ops.kraus_to_choi
toqito.channel_ops.partial_channel
toqito.channel_ops.dual_channel
.. toctree::
.. autosummary::
:toctree: _autosummary
toqito.channel_props.is_completely_positive
toqito.channel_props.is_herm_preserving
toqito.channel_props.is_positive
toqito.channel_props.is_trace_preserving
toqito.channel_props.is_unital
toqito.channel_props.choi_rank
toqito.channel_props.is_quantum_channel
toqito.channel_props.is_unitary