Characterizing Kadison--Schwarz maps on $M_3$

• URL: http://arxiv.org/abs/2512.18900v2
• Date: Tue, 23 Dec 2025 19:13:37 GMT
• Title: Characterizing Kadison--Schwarz maps on $M_3$
• Authors: Adam Rutkowski,
• Abstract summary: We analyze unital linear maps on $M_3$ using the Bloch--Gell--Mann representation.<n>We derive explicit analytic conditions ensuring the Kadison--Schwarz property.
• Score: 0.6091702876917281
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Kadison--Schwarz (KS) maps form a natural class of positive linear maps lying tweet positivity and complete positivity. Despite their relevance in quantum dynamics and operator algebras, a detailed analytic characterization of KS maps is still largely lacking. In this work we analyze unital linear maps on $M_3$ using the Bloch--Gell--Mann representation. Exploiting unitary equivalence and structural properties of the $\mathfrak{su}(3)$ algebra, we derive explicit analytic conditions ensuring the Kadison--Schwarz property. Our approach clarifies the relation between KS maps and completely positive maps on $M_3$.

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