On unital qubit channels

2023/01/03 by Chi-Kwong Li, Man-Duen Choi, Li, Chi-Kwong +1 · 2 citations
Computer Science · Mathematics · #15B57 #47B65 #81Q10 #Algebraic structures and combinatorial models #FOS: Physical sciences #Graph theory and applications #Matrix Theory and Algorithms #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2301.01358

openalex publication_date 2023/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 form a complete set of invariants 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 p₁, …, p_m as long as 2(p₁, …, p_m) is majorized by the vector of eigenvalues of the Choi matrix of the channel. A unital qubit channel in the canonical form will transform the Bloch sphere onto an ellipsoid. We look into the detailed structure of the natural linear maps sending the Bloch sphere onto a corresponding ellipsoid.

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