Markovian dynamics of single-rebit open quantum systems and information-theoretic analysis of color perception
Résumé
This paper is devoted to the study of the Markovian dynamics of open two-state quantum systems defined over the real numbers. Its aim is twofold. On the one hand, we provide a complete mathematical description of such dynamics when the affine component of the quantum channel semigroup is Markovian. We describe Lindblad and Kraus operators, orthogonal evolutions by means of Jordan algebra derivations, as well as solutions of the GKSL dissipative equation and their effect on the relative entropy. On the other hand, we are interested in an original application to color perception that motivates this analysis. Using a recent novel model in which perceived colors are given by Lüders measurements on the state space of a rebit, we show how the chromatic distortion induced by a non-neutral illuminant can be modeled by a Markovian rebit channel that progressively reduces color distinguishability. This colorimetric effect is illustrated through simulations on digital images, offering a concrete demonstration of the relevance of Markovian rebit evolution for modeling perceptual phenomena.
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