Optimal convex approximation of quantum channels based on $α$-affinity

• URL: http://arxiv.org/abs/2606.05745v1
• Date: Thu, 04 Jun 2026 06:18:32 GMT
• Title: Optimal convex approximation of quantum channels based on $α$-affinity
• Abstract summary: We develop a unified framework for optimal convex approximation of quantum channels based on the quantum $$-affinity measure.<n>We derive analytical solutions for the optimal convex approximation of single-qubit unitary channels over both the SU(2)-covariant and Pauli channel families.<n>In contrast to conventional approaches based on the diamond norm, our framework provides a systematic and analytically tractable approach to quantum channel approximation under realistic constraints.
• Score: 0.7202365483397896
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Determining the minimal distance between a target channel and a convex hull of predefined set of implementable channels is a fundamental problem in quantum resource theory, and provides key guidance for experimental implementations. In this work, we develop a unified analytical framework for optimal convex approximation of quantum channels based on the quantum $α$-affinity measure. We construct a channel distance metric induced by the α-affinity and the ChoiJamiolkowski isomorphism, which satisfies the required properties of a well-defined channel distance. Subsequently, we present an optimization framework for the convex approximation of quantum channels, and derive analytical solutions for the optimal convex approximation of single-qubit unitary channels over both the SU(2)-covariant and Pauli channel families, obtaining closed-form expressions for the optimal parameters and the minimal approximation distance. This framework is further applied to the amplitude-damping channel, yielding the explicit form of its optimal approximation and the associated minimal α-affinity distance. In contrast to conventional approaches based on the diamond norm, our framework provides a systematic and analytically tractable approach to quantum channel approximation under realistic constraints.

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