cirq.kraus_to_choi
Returns the unique Choi matrix corresponding to a Kraus representation of a channel.
cirq.kraus_to_choi(
kraus_operators: Sequence[np.ndarray]
) -> np.ndarray
Used in the notebooks
Quantum channel E: L(H1) -> L(H2) may be described by a collection of operators A_i, called
Kraus operators, such that
$$
E(\rho) = \sum_i A_i \rho A_i^\dagger.
$$
Kraus representation is not unique. Alternatively, E may be specified by its Choi matrix J(E)
defined as
$$
J(E) = (E \otimes I)(|\phi\rangle\langle\phi|)
$$
where \(|\phi\rangle = \sum_i|i\rangle|i\rangle\) is the unnormalized maximally entangled state
and I: L(H1) -> L(H1) is the identity map. Choi matrix is unique for a given channel.
The computation of the Choi matrix from a Kraus representation is essentially a reconstruction
of a matrix from its eigendecomposition. It has the cost of O(kd**4) where k is the number of
Kraus operators and d is the dimension of the input and output Hilbert space.
Args |
kraus_operators
|
Sequence of Kraus operators specifying a quantum channel.
|
Returns |
Choi matrix of the channel specified by kraus_operators.
|
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Last updated 2024-06-27 UTC.
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