arXiv subjects

Edoardo Provenzi

Publications and source records attributed to Edoardo Provenzi.

12 recordsLinked to original sources

arXiv2026

Markovian dynamics of single-rebit open quantum systems with applications to colour perception

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.

quant-ph↗

arXiv2025

A Perceptually Inspired Variational Framework for Color Enhancement

Basic phenomenology of human color vision has been widely taken as an inspiration to devise explicit color correction algorithms. The behavior of these models in terms of significative image features (such as contrast and dispersion) can be difficult to characterize. To cope with this, we propose to use a variational formulation of color contrast enhancement that is inspired by the basic phenomenology of color perception. In particular, we devise a set of basic requirements to be fulfilled by an energy to be considered as `perceptually inspired', showing that there is an explicit class of functionals satisfying all of them. We single out three explicit functionals that we consider of basic interest, showing similarities and differences with existing models. The minima of such functionals is computed using a gradient descent approach. We also present a general methodology to reduce the computational cost of the algorithms under analysis from ${\cal O}(N^2)$ to ${\cal O}(N\log N)$, being $N$ the number of input pixels.

cs.CV↗

arXiv2025

An Operational Quantum Information Framework for Experimental Studies on Color Perception

Starting from the foundational axiomatization of the perceptual color space initiated by Schr\"odinger in 1920 and eventually refined by Resnikoff in 1974, Berthier, Provenzi and their collaborators have recently proposed a reformulation of perceptual color attributes within the framework of quantum information. Their work is based on the Jordan algebra formalism of quantum theories and, more specifically, on a quantum system described by a spin factor over the field of real numbers. This theoretical framework is not that of ordinary quantum mechanics, mainly because it requires dealing with rebits, whereas the latter uses qubits. The aim of this paper is to show that this difference in no way hinders the implementation of experimental protocols for testing the validity of the predictions of the color perception model. In particular, we show how to compute the quantum information based perceptual attributes of perceived colors in terms of qubit density matrices.

q-bio.NC↗

arXiv2025

On the Monotonicity of relative entropy: A Comparative Study of Petz's and Uhlmann's Approaches

We revisit the monotonicity of relative entropy under the action of quantum channels, a foundational result in quantum information theory. Among the several available proofs, we focus on those by Petz and Uhlmann, which we reformulate within a unified, finite-dimensional operator-theoretic framework. In the first part, we examine Petz's strategy, identify a subtle flaw in his original use of Jensen's contractive operator inequality, and point out how it was corrected to restore the validity of his line of reasoning. In the second part, we develop Uhlmann's approach, which is based on interpolations of positive sesquilinear forms and applies automatically also to non-invertible density operators. By comparing these two approaches, we highlight their complementary strengths: Petz's method is more direct and clear, Uhlmann's is more abstract and general. Our treatment aims to clarify the mathematical structure underlying the monotonicity of relative entropy and to make these proofs more accessible to a broader audience interested in both the foundations and the applications of quantum information theory.

quant-ph↗

arXiv2025

The classification of rebit quantum channels

The classification of qubit channels is known since 2002. However, that of rebit channels has never been studied so far, maybe because of the scarcity of concrete rebit examples. In this paper we point out that the strategy used to classify qubit channels cannot be pursued in the rebit case and we propose an alternative which allows us to complete the rebit channel classification. This mathematical result has not only a purely abstract interest: as we shall briefly mention, it may have applications in the analysis of local properties and temporal evolution of real quantum systems and also in a recent color vision model based on quantum information.

quant-ph↗

arXiv2025

Geometry of color perception. Part 1: Structures and metrics of a homogeneous color space

This is the first half of a two-part paper dealing with the geometry of color perception. Here we analyze in detail the seminal 1974 work by H.L. Resnikoff, who showed that there are only two possible geometric structures and Riemannian metrics on the perceived color space P compatible with the set of Schrödinger's axioms completed with the hypothesis of homogeneity. We recast Resnikoff's model into a more modern colorimetric setting, provide a much simpler proof of the main result of the original paper and motivate the need of psychophysical experiments to confute or confirm the linearity of background transformations, which act transitively on P. Finally, we show that the Riemannian metrics singled out by Resnikoff through an axiom on invariance under background transformations are not compatibles with the crispening effect, thus motivating the need of further research about perceptual color metrics.

q-bio.NC↗

arXiv2025

Split-quaternions for perceptual white balance

We propose a perceptual chromatic adaptation transform for white balance that makes use of split-quaternions. The novelty of the present work, which is motivated by a recently developed quantum-like model of color perception, consists at stressing the link between the algebraic structures appearing in this model and a certain sub-algebra of the split-quaternions. We show the potentiality of this approach for color image processing applications by proposing a chromatic adaptation transform, implemented via an appropriate use of the split-quaternion multiplication. Moreover, quantitative comparisons with the widely used state-of-the art von Kries chromatic adaptation transform are provided.

eess.IV↗

arXiv2025

The relativity of color perception

Physical colors, i.e. reflected or emitted lights entering the eyes from a visual environment, are converted into perceived colors sensed by humans by neurophysiological mechanisms. These processes involve both three types of photoreceptors, the LMS cones, and spectrally opponent and non-opponent interactions resulting from the activity rates of ganglion and lateral geniculate nucleus cells. Thus, color perception is a phenomenon inherently linked to an experimental environment (the visual scene) and an observing apparatus (the human visual system). This is clearly reminiscent of the conceptual foundation of both relativity and quantum mechanics, where the link is between a physical system and the measuring instruments. The relationship between color perception and relativity was explicitly examined for the first time by the physicist H. Yilmaz in 1962 from an experimental point of view. The main purpose of this contribution is to present a rigorous mathematical model that, by taking into account both trichromacy and color opponency, permits to explain on a purely theoretical basis the relativistic color perception phenomena argued by Yilmaz. Instead of relying directly on relativistic considerations, we base our theory on a quantum interpretation of color perception together with just one assumption, called trichromacy axiom, that summarizes well-established properties of trichromatic color vision within the framework of Jordan algebras. We show how this approach allows us to reconcile trichromacy with Hering's opponency and also to derive the relativistic properties of perceived colors without any additional mathematical or experimental assumption.

q-bio.NC↗

arXiv2025

A quantum information-based refoundation of color perception concepts

In this paper we deal with the problem of overcoming the intuitive definition of several color perception attributes by replacing them with novel mathematically rigorous ones. Our framework is a quantum-like color perception theory recently developed, which constitutes a radical change of view with respect to the classical CIE models and their color appearance counterparts. We show how quantum information concepts, as e.g. effects, generalized states, post-measurement transformations and relative entropy provide tools that seem to be perfectly fit to model color perception attributes as brightness, lightness, colorfulness, chroma, saturation and hue. An illustration of the efficiency of these novel definitions is provided by the rigorous derivation of the so-called lightness constancy phenomenon.

q-bio.NC↗

arXiv2025

Quantum measurement and color perception: theory and applications

In this paper we make a systematic use of the quantum measurement theory to describe perceived colors and analyze some of their fundamental properties. After motivating the naturalness of the quantum measurement approach in the mathematical framework of the color perception theory proposed by the authors in previous papers, we show how to obtain several results. Among our theoretical outcomes, we mention the possibility to confine the color cone to a finite-volume color solid and the link between post-measurement state changes, Lorentz boosts and the Einstein-Poincaré relativistic addition law. We apply these results to obtain a chromatic match equation that emphasizes the importance of the Hilbert-Klein metric on the unit disk and we also present a quantitative description of Hunt's effect.

q-bio.NC↗

arXiv2025

The quantum nature of color perception: Uncertainty relations for chromatic opposition

In this paper we provide an overview on the foundation and first results of a very recent quantum theory of color perception, together with novel results about uncertainty relations for chromatic opposition. The major inspiration for this model is the 1974 remarkable work by H.L. Resnikoff, who had the idea to give up the analysis of the space of perceived colors through metameric classes of spectra in favor of the study of its algebraic properties. This strategy permitted to reveal the importance of hyperbolic geometry in colorimetry. Starting from these premises, we show how Resnikoff's construction can be extended to a geometrically rich quantum framework, where the concepts of achromatic color, hue and saturation can be rigorously defined. Moreover, the analysis of pure and mixed quantum chromatic states leads to a deep understanding of chromatic opposition and its role in the encoding of visual signals. We complete our paper by proving the existence of uncertainty relations for the degree of chromatic opposition, thus providing a theoretical confirmation of the quantum nature of color perception.

q-bio.NC↗

arXiv2001

Inductive Construction of the Loop Transform for Abelian Gauge Theories

We construct the loop transform in the case of Abelian gauge theories as unitary operator given by the inductive limit of Fourier transforms on tori. We also show that its range, i.e.the space of kinematical states of the quantum loop representation, is the Hilbert space of square integrable complex valued functions on the group of loops.

math-ph↗