aiqbench analysis
This research establishes a rigorous mathematical framework for Markovian dynamics in real-number quantum systems (rebits), explicitly identifying Lindblad generators for these channels. The study demonstrates practical utility by modeling chromatic distortion and color vision deficiencies through simulations, bridging abstract quantum classification with tangible applications in visual perception. While theoretically significant, the work remains a foundational theoretical contribution rather than a deployable product or immediate industrial solution.
Markovian dynamics of single-rebit open quantum systems with applications to colour perception
arXiv:2606.08117v1 Announce Type: new Abstract: This paper investigates the Markovian dynamics of open two-state quantum systems defined over the real numbers (rebits). Two main objectives are pursued. First, we present a comprehensive classification of Markovian rebit quantum channels, i.e. one-parameter semigroups of completely positive, trace-preserving (CPTP) maps acting on the rebit state space. We show that a full characterisation of their action can be achieved and that describing these channels as solutions of the GKSL equation allows us to explicitly identify the associated Lindblad generators and conditions for complete positivity. Second, we present an original application of this classification to colour perception. Using a recent model in which perceived colours arise from L\"uders measurements on the rebit state space, we show how chromatic distortion induced by a non-neutral illuminant can be modelled by a Markovian rebit channel that progressively diminishes colour distinguishability. Other types of channels could be used to study colour vision deficiencies. These phenomena are illustrated by simulations on digital images, highlighting the relevance of rebit Markovian dynamics in modelling colour vision.
Abstract:This paper investigates the Markovian dynamics of open two-state quantum systems defined over the real numbers (rebits). Two main objectives are pursued. First, we present a comprehensive classification of Markovian rebit quantum channels, i.e. one-parameter semigroups of completely positive, trace-preserving (CPTP) maps acting on the rebit state space. We show that a full characterisation of their action can be achieved and that describing these channels as solutions of the GKSL equation allows us to explicitly identify the associated Lindblad generators and conditions for complete positivity. Second, we present an original application of this classification to colour perception. Using a recent model in which perceived colours arise from Lüders measurements on the rebit state space, we show how chromatic distortion induced by a non-neutral illuminant can be modelled by a Markovian rebit channel that progressively diminishes colour distinguishability. Other types of channels could be used to study colour vision deficiencies. These phenomena are illustrated by simulations on digital images, highlighting the relevance of rebit Markovian dynamics in modelling colour vision.
arXiv:2606.08117 [quant-ph]
(or arXiv:2606.08117v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.08117 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
https://doi.org/10.1007/s10773-026-06379-1 Focus to learn more DOI(s) linking to related resources
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