Geometric analysis of a class of interpolating quantum maps for d-level systems shows trajectories crossing positivity regions with eventual entanglement breaking and interpretations for divisibility and eternal non-Markovianity.
Tomiyama-type maps with a diagonal perturbation
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abstract
We investigate a two-parameter family of linear maps on matrix algebras, constructed as diagonal perturbations of classical Tomiyama maps. Employing the Choi matrix method alongside block-positivity techniques, we derive explicit necessary and sufficient conditions for positivity, complete positivity, and k-positivity across arbitrary dimensions. These conditions provide a transparent geometric characterization of the positivity regions within the parameter space.
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quant-ph 1years
2026 1verdicts
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Interpolating between positive, Schwarz, and completely positive evolution for d-level systems
Geometric analysis of a class of interpolating quantum maps for d-level systems shows trajectories crossing positivity regions with eventual entanglement breaking and interpretations for divisibility and eternal non-Markovianity.