Channels
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
such that \(\Phi\) is completely positive and trace preserving.
Distance Metrics for Quantum Channels
Compute the channel fidelity between two quantum channels [VW20]. |
Quantum Channels
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Produce the Choi channel or one of its generalizations [Choi92]. |
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Produce the partially dephasing channel [WatDeph18]. |
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Produce the partially depolarizing channel [WikDepo], [WatDepo18]. |
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Compute the partial trace of a matrix [WikPtrace]. |
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Compute the partial transpose of a matrix [WikPtrans]. |
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Compute the realignment of a bipartite operator [LAS08]. |
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Produce the reduction map or reduction channel. |
Operations on Quantum Channels
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Apply a quantum channel to an operator [WatAChan18]. |
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Compute a list of Kraus operators from the Choi matrix [Rigetti20]. |
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Compute the Choi matrix of a list of Kraus operators [WatKraus18]. |
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Apply channel to a subsystem of an operator [WatPMap18]. |
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Compute the dual of a map (quantum channel) [WatDChan18]. |
Properties of Quantum Channels
Determine whether the given channel is completely positive [WatCP18]. |
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Determine whether the given channel is Hermitian-preserving [WatH18]. |
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Determine whether the given channel is positive [WatPM18]. |
Determine whether the given channel is trace-preserving [WatTP18]. |
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Determine whether the given channel is unital [WatUnital18]. |
Calculate the rank of the Choi representation of a quantum channel [WatChoiRank18]. |
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Determine whether the given input is a quantum channel [WatQC18]. |
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Given a quantum channel, determine if it is unitary [WatIU18]. |