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# cirq.qis.kraus_to_choi

Returns the unique Choi matrix corresponding to a Kraus representation of a channel.

### Used in the notebooks

Used in the tutorials

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.

kraus_operators Sequence of Kraus operators specifying a quantum channel.

Choi matrix of the channel specified by kraus_operators.

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[{ "type": "thumb-up", "id": "easyToUnderstand", "label":"Easy to understand" },{ "type": "thumb-up", "id": "solvedMyProblem", "label":"Solved my problem" },{ "type": "thumb-up", "id": "otherUp", "label":"Other" }]