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Article overview
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On unital qubit channels | Chi-Kwong Li
; Man-Duen Choi
; | Date: |
3 Jan 2023 | Abstract: | A canonical form for unital qubit channels under local unitary transforms is
obtained. In particular, it is shown that the eigenvalues of the Choi matrix of
a unital quantum channel are complete invariant of the canonical form. It
follows immediately that every unital qubit channel is the average of four
unitary channels. More generally, a unital qubit channel can be expressed as
the convex combination of unitary channels with convex coefficients $p_1,
dots, p_m$ as long as $(p_1, dots, p_m)$ is majorized by the vector of
eigenvalues of the Choi matrix of the channel. By the fact that every unital
map $Phi$ on $2 imes 2$ matrices preserving trace and Hermitian matrices
corresponds to a linear map $phi$ on ${mathbb R}^3$ that will transform the
Bloch (unit) sphere in ${mathbb R}^3$ to an ellipsoid ${mathcal E}$, it is
shown that $Phi$ is a unital qubit channel if and only if $phi$ is a convex
combination of special orthogonal matrices. | Source: | arXiv, 2301.01358 | Services: | Forum | Review | PDF | Favorites |
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