cirq.kraus_to_choi

View source on GitHub

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.