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
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.. 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
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.. 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
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.. 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